# Archivio 2022

2022
01 Ottobre
Liliana Albertazzi
Experimental aesthetics in perceptual organisation
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
29 Settembre
Stefano Canino
Complete intersections on Veronese surfaces

seminario di algebra e geometria

In “Commentationes Geometricae” Euler asked when a sets of points in the plane is the intersection of two curves, that is, using the modern terminology, when a set of points in the plane is a complete intersection. In the same period, Cramer asked similar questions so that this type of questions is presently known as the Cramer-Euler problem. In this paper, we consider a generalization of the Cramer-Euler problem: characterize the possible complete intersections lying on a Veronese surface, and more generally on a Veronese variety. The main result describes all possible reduced complete intersections on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of the quadratic Veronese threefold. Our main tool is an effective characterization of all possible Hilbert functions of reduced subvarieties of Veronese surfaces.
2022
28 Settembre
Kelin Xia
Mathematical AI for molecular data analysis

seminario interdisciplinare

Artificial intelligence (AI) based molecular data analysis has begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all AI-based learning models is the efficient molecular representations and featurization. Here we propose advanced mathematics-based molecular representations and featurization (or feature engineering). Molecular structures and their interactions are represented as various simplicial complexes (Rips complex, Neighborhood complex, Dowker complex, and Hom-complex), hypergraphs, and Tor-algebra-based models. Molecular descriptors are systematically generated from various persistent invariants, including persistent homology, persistent Ricci curvature, persistent spectral, and persistent Tor-algebra. These features are combined with machine learning and deep learning models, including random forest, CNN, RNN, Transformer, BERT, and others. They have demonstrated great advantage over traditional models in drug design and material informatics.
2022
27 Settembre
S. Mukherjee
Transfer of knowledge: Quasilinear equations in Carnot groups
nel ciclo di seminari: GHAIA MEETING

seminario di analisi matematica

Transfer of knowledge: open only to members of the project
2022
27 Settembre
S. Mukherjee
Transfer of knowledge: Quasilinear equations in the Heisenberg group
nell'ambito della serie: GHAIA SEMINARS

seminario di analisi matematica

Transfer of knowledge open only to the members of the project
2022
20 Settembre
Giovanni Cupini
The regularity of solutions to elliptic systems in divergence form
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022

seminario di analisi matematica

The theory of elliptic equations and systems of m equations in divergence form, is strictly related to the theory of minimization of integral functionals. After a review on the existence issue, we will focus on the regularity problem: under which conditions the solutions are regular? The ideal process to prove that a (weak) solution, apriori only in a Sobolev space W^{1,p}, is C^{\infty} will be sketched. Unfortunately, the gain in regularity is not for free, and it is guaranteed only if particular conditions are met. In the past years, counterexamples have shown that: 1) under certain growth conditions the regularity can be lost, even in the scalar case; 2) in the vectorial case the situation is far worse, since even solutions to linear and uniformly elliptic systems may be locally unbounded (!). The main effort is to find conditions that force the regularity of the solutions. We will focus in particular to the vectorial case; i.e. the local regularity of weak solutions to elliptic systems. The main and most common structure condition, that forces, in general, regularity in the vectorial setting, is the so called Uhlenbeck’s structure (dependence on the modulus of the gradient). Meier, in 1982, introduced another assumption, related to a so called Indicator function: a more general condition than Uhlenbeck’s one, that allows to include more general systems. For them, Meier proved the local boundedness of the solutions. We will exhibit examples of systems that do not satisfy the Meier’s condition, but for which, in a recent result in collaboration with F. Leonetti (L’Aquila) and E. Mascolo (Firenze), we proved the boundedness of the solutions. The crucial structure assumption is the componentwise coercivity introduced by Bjorn in 2001.
2022
20 Settembre
Nicola Pagani
A wall-crossing formula for universal Brill-Noether cycles
nel ciclo di seminari: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

We will discuss an explicit graph formula, in terms of boundary strata classes, for the wall-crossing of universal (over Mbargn) Brill-Noether classes. More precisely, fix two stability conditions and for universal compactified Jacobians that are on different sides of a wall in the stability space. Then we can compare the two universal Brill-Noether classes on the two compactified Jacobians by pulling one of them back along the (rational) identity map. The calculation involves constructing a resolution by means of subsequent blow-ups. If time permits, we will discuss the significance of our formula and potential applications. This is joint with Alex Abreu.
2022
12 Settembre
Simona Perotto, MOX - Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano
"Free-form design of structures and materials driven by innovative topology optimization techniques".
nell'ambito della serie: AM^2 SEMINARS

seminario di analisi numerica

2022
09 Settembre
Paolo Aschieri
Atiyah sequences of braided Lie algebras and their splittings

seminario di algebra e geometria, fisica matematica

We discuss Atiyah sequences of braided Lie algebras and their splittings
2022
09 Settembre
Mauro Mantegazza
Jet functors in noncommutative geometry

seminario di algebra e geometria

We construct an infinite family of endofunctors $J^n_d$ on the category of left $A$-modules, where $A$ is a unital associative algebra over a commutative ring $k$, equipped with an exterior algebra $\Omega^\bullet_d$. We prove that these functors generalize the corresponding classical notion of jet functors. The functor $J^n_d$ comes equipped with a natural transformation from the identity functor to itself, which plays the role of the classical prolongation map. This allows us to define the notion of linear differential operator with respect to $\Omega^\bullet_d$. These retain most classical properties of differential operators, and operators such as partial derivatives and connections belong to this class. Moreover, we construct a functor of quantum symmetric forms $S^n_d$ associated to $\Omega^\bullet_d$, and proceed to introduce the corresponding noncommutative analogue of the Spencer $\delta$-complex. We give necessary and sufficient conditions under which the jet functor $J^n_d$ satisfies the jet exact sequence, $0\to S^n_d \to J^n_d \to J^{n−1}_d \to 0$. This involves imposing mild homological conditions on the exterior algebra, in particular on the Spencer cohomology $H^{\bullet,2}$. This is a joint work with K. Flood and H- Winther.
2022
09 Settembre
Andrea Santi
Exceptionally simple super-PDE

seminario di algebra e geometria

In 1893, Cartan and Engel gave the first realizations of the exceptional simple Lie algebra G(2) as symmetry algebra of various geometric structures. I will report on generalizations of this story to the exceptional simple Lie superalgebras G(3) and F(4), in particular on a supersymmetric extension of the Hilbert–Cartan equation. Joint works with Kruglikov & The
08/09/2022
09/09/2022
Elisa Affili
Decay estimates in evolution equations with classical and fractional time-derivatives

seminario di analisi matematica

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, and diffusion operators as the classic and fractional Laplacian, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation. This work was done in collaboration with Enrico Valdinoci.
08/09/2022
09/09/2022
Stefano Biagi
A Brezis-Nirenberg type result for mixed local and nonlocal operators

seminario di analisi matematica

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08/09/2022
09/09/2022
Claudia Bucur
Relazione all'interno del convegno: Nonlocal and Nonlinear Partial Differential Equations at the University of Bologna

seminario di analisi matematica

08/09/2022
09/09/2022
Matteo Cozzi
Blowing-up solutions for a nonlocal Liouville type equation in a union of intervals

seminario di analisi matematica

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08/09/2022
09/09/2022
Martina Magliocca
Some fourth order problems arising in Physics

seminario di analisi matematica

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08/09/2022
09/09/2022
Edoardo Proietti Lippi
Nonlocal Neumann boundary conditions

seminario di analisi matematica

We present some properties of a nonlocal version of the Neumann boundary conditions associated to problems involving the fractional p-Laplacian. For this problems, we show some regularity results for the general case and some existence results for particular types of problems. When p=2, we give a generalization of the boundary conditions in which both the nonlocal and the classic Neumann conditions are present, and we consider problems involving both nonlocal and local interactions.
08/09/2022
09/09/2022
Alberto Roncoroni
Rigidity results for the critical p-Laplace equation

seminario di analisi matematica

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08/09/2022
09/09/2022
Delia Schiera
Maximum principles and related problems for a class of nonlocal extremal operators

seminario di analisi matematica

I will consider a class of degenerate nonlinear operators that are extremal among operators with one dimensional fractional diffusion and that approximate the so-called truncated Laplacians. I will show some properties of these operators, emphasizing the differences both with the local equivalent operators and with more standard nonlocal operators such as the fractional Laplacian. In particular, continuity properties, validity of comparison and maximum principles, and their relation with principal eigenvalues, will be presented. Joint work with Isabeau Birindelli and Giulio Galise.
2022
06 Settembre
Emanuele Mingione
TOC4Deep
nell'ambito della serie: SEMINARI MAT/08 TEAM

seminario di analisi numerica, fisica matematica

2022
06 Settembre
Emanuele Mingione
TOC4Deep
nell'ambito della serie: SEMINARI MAT/08 TEAM

seminario di analisi numerica, fisica matematica

2022
01 Settembre
Tomoshige Yukita
Arithmetic nature and continuity of growth rates of Coxeter systems

seminario di algebra e geometria

First, I will talk about the space of Coxeter systems and show that the growth rate is a continuous function on the space. This result on the continuity of the growth rates is a geometric group theoretic extension of the results on the growth of hyperbolic Coxeter groups of dimension 2 and 3 proved by Floyd and Kolpakov. Second, I will explain an application of the result on the continuity to the study of arithmetic nature of growth rates of Coxeter systems. The second part of this talk is based on joint work with Naomi Bredon.
2022
22 Agosto
Juan Manfredi, Pittsburgh University
The Infinity-Laplacian relative to vector fields

seminario di analisi matematica

2022
29 Luglio
Daniela De Silva, Columbia University, New York
Regularity Theory for Elliptic equations: (VI) Conclusive remarks and if time and students' preparation allows it, the Dirichlet problem for the minimal surface equation.
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

Holder regularity of weak solutions to divergence and non-divergence elliptic equations. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
29 Luglio
Daniela De Silva, Columbia University, New York
Regularity Theory for Elliptic equations: (V) Weak Harnack Inequality
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

Holder regularity of weak solutions to divergence and non-divergence elliptic equations. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
28 Luglio
Daniela De Silva, Department of Mathematics Barnard College Columbia University, New York
The Alt-Phillips functional for negative powers

seminario di analisi matematica

2022
28 Luglio
Daniela De Silva, Columbia University, New York
The Alt-Phillips functional for negative powers
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

2022
28 Luglio
Daniela De Silva, Columbia University, New York
Regularity Theory for Elliptic equations: (IV) ABP Estimates
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

ABP Estimates. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
28 Luglio
Daniela De Silva, Columbia University, New York
Regularity Theory for Elliptic equations: (III) Harnack Inequality
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

Holder regularity of weak solutions to divergence and non-divergence elliptic equations. (III) Harnack Inequality. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
27 Luglio
Daniela De Silva , Columbia University, New York
Regularity Theory for Elliptic equations : (II) De Giorgi- Nash-Moser Theorem
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

Holder regularity of weak solutions to divergence and non-divergence elliptic equations. (II) De Giorgi- Nash-Moser Theorem. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
27 Luglio
Francesco Galluppi
Defectivity of Segre-Veronese varieties
nel ciclo di seminari: GEOMETRIA ALGEBRICA E TENSORI

seminario di algebra e geometria

Secant defectivity of projective varieties is classically approached via dimensions of linear systems with multiple base points in general position. The latter can be studied via degenerations. We exploit a technique that allows some of the base points to collapse together. We deduce a general result which we apply to prove a conjecture by Abo and Brambilla: for c≥3 and d≥3, the Segre-Veronese embedding of Pm×Pn in bidegree (c,d) is non-defective.
2022
27 Luglio
Daniela De Silva, Columbia University, New York
Regularity Theory for Elliptic equations: (I) Introduction and Preliminaries
nel ciclo di seminari: CORSO DI DOTTORATO

seminario di analisi matematica

Introduction and Preliminaries Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.
2022
13 Luglio
Andrew Waldron
Dynamical Quantization of Contact Structures

seminario di algebra e geometria, fisica matematica

In this talk we expalin how to construct a dynamical quantization for contact manifolds in terms of a flat connection acting on a Hilbert tractor bundle. We show that this contact quantization, which is independent of the choice of contact form, can be obtained by quantizing the Reeb dynamics of an ambient strict contact manifold equivariantly with respect to an R+-action. The contact quantization further determines a certain contact tractor connection whose parallel sections determine a distinguished choice of Reeb dynamics and their quantization. This relationship relies on tractor constructions from parabolic geometries and mirrors the tight relationship between Einstein metrics and conformal geometries.
2022
06 Luglio
Andrea Asperti
TOC4DEEP - SECOND ONLINE-ONSITE WORKSHOP
nell'ambito della serie: SEMINARI MAT/08 TEAM

seminario di analisi numerica

As part of the Una Europa funded grant TOC4Deep (Tensor-based Optimal Control Approaches for Deep Learning) a series of half-day workshops will be held over the next 6 months to encourage scientific networking and discussions between the project universities of Edinburgh, Bologna and KU Leuven. The second of these workshops will take place on Wednesday 06th July, with a main focus on computer scientists' perspective on machine and deep learning. The workshop will be hybrid, with in person attendance in Seminario II, Dipartimento di Matematica, University of Bologna, or via Zoom.
2022
05 Luglio
Lorenzo Ruffoni
Special cubulation of strict hyperbolization
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Hyperbolization procedures are constructions that turn a simplicial complex into a metric space of non-positive curvature. They were first introduced by Gromov, and later refined by Charney and Davis to produce spaces of strictly negative curvature. In the first part of the talk I will describe some notions of curvature, some hyperbolization procedures, and then showcase some applications in the theory of manifolds. In the second part of the talk I will present joint work with J. Lafont, in which we show that, while the spaces obtained via hyperbolization are often topologically exotic, their fundamental groups are as nice as possible. Namely, these groups admit nice actions on cubical complexes, and are therefore linear over the integers. As an application, we obtain new examples of hyperbolic groups that algebraically fiber.
29/06/2022
01/07/2022
Barak Weiss
Relazione all'interno del convegno: Geometry and Dynamics of Moduli Spaces

seminario di sistemi dinamici

TBA
29/06/2022
01/07/2022
Jonathan Chaika
Relazione all'interno del convegno: Geometry and Dynamics of Moduli Spaces

seminario di sistemi dinamici

TBA
29/06/2022
01/07/2022
Pascal Hubert
Relazione all'interno del convegno: Geometry and Dynamics of Moduli Spaces

seminario di sistemi dinamici

TBA
29/06/2022
01/07/2022
Erwan Lanneau
Relazione all'interno del convegno: Geometry and Dynamics of Moduli Spaces

seminario di sistemi dinamici

TBA
2022
28 Giugno
Justin Sawon
Mirror symmetry for generalized Kummer varieties
nel ciclo di seminari: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The generalized Kummer variety K_n of an abelian surface A is the fibre of the natural map Hilb^{n+1}A->Sym^{n+1}A->A. Debarre described a Lagrangian fibration on K_n whose fibres are the kernels of JacC->A, where C are curves in a fixed linear system in A. In this talk we consider the dual of the Debarre system, constructed in a similar way to the duality between SL- and PGL-Hitchin systems described by Hausel and Thaddeus. We conjecture that these dual fibrations are mirror symmetric, in the sense that their (stringy) Hodge numbers are equal, and we verify this in a few cases. In fact, there is another isotrivial Lagrangian fibration on K_n. We can describe its dual fibration and verify the mirror symmetry relation in many more cases.
2022
24 Giugno
Simone Billi
Hyperkähler fourfolds with an action of A7

seminario di algebra e geometria

Compact Hyperkähler manifolds (also called Irreducible Holmorphic Symplectic) are of great interest because of the famous classification theorem of complex manifold with vanishing first Chern class and for the very rich structure on the second cohomology. Most of the geometrical information is in fact recovered by the data of the Hodge decomposition in degree two and its relation with the lattice structure on the integral second cohomology. Due to their rigidity, very few examples have been found and it is very not known if indeed there are others. A family of Hyperkähler fourfolds arise as double covers of EPW sextics associated with a certain Lagrangian space. In a joint work with T. Wawak we construct two quite explicit examples of such fourfolds with a symplectic action of the alternating group A7. These are polarized manifolds with polarization 2 and from a classification of the possible automorphisms only two such examples are expected, but no information on the Picard lattice is available so we are not able to distinguish them yet.
2022
24 Giugno
Luca Capogna
The Neumann problem and the fractional laplacian in measure metric spaces

seminario di analisi matematica

In this talk we will report on some recent joint work with Josh Kline, Riikka Korte, Marie Snipes and Nages Shanmugalingam, concerning the Neumann problem in PI spaces, and a new definition of fractional p-Laplacians in arbitrary doubling measure metric space. We extend some earlier work by Lukas Maly and Nages Shanmugalingam, proving well posedness in appropriate Lebesgue classes for the Neumann problem for p-Laplacians, and then leverage these results to prove existence, stability and regularity for the corresponding non homogeneous non-local PDE.
2022
23 Giugno
From configurations on graphs to high dimensional cohomology of moduli spaces M_{2,n}
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The moduli spaces of algebraic curves with marked points have hugely complicated and interesting cohomology. While in low dimensions the cohomology exhibits a form of (representation-) stability, near the top dimension very little is known. Tropical geometry gives access to some of this high dimensional cohomology, namely its top weight quotient. In joint work with Bibby, Chan, Yun and Hainaut we relate the top weight cohomology of the moduli space of genus 2 curves with marked points with that of a configuration space on a graph, opening the door to extensive new calculations and qualitative analyses.
2022
21 Giugno
Martino Lupini
Anche i gruppi polacchi hanno un cuore

seminario interdisciplinare

L'algebra omologica e' stata sviluppata classicamente nel contesto generale di categorie abeliane. Sfortunatamente molte categorie importanti in analisi, geometria, e teoria dei numeri non sono abeliane ma solo quasi-abeliane. Per ovviare a questo problema, Belininson, Berenstein, e Deligne descrissero nel 1982 il "completamento abeliano" di una categoria quasi-abeliana arbitraria, detto cuore. In teoria, questo permetterebbe di ridursi al caso di categorie abeliane. Un ostacolo nell'applicazione di tale costruzione e' dato dal fatto che produce in generale una categoria astratta, i cui morfismi sono difficili da descrivere. In questo seminario spieghero' come metodi di logica, ed in particolare teoria descrittiva degli insiemi, permettano di dare una descrizione come categoria concreta del cuore di molteplici categorie quasi-abeliane di fondamentale importanza in analisi, geometria, e teoria dei numeri, tra cui: gruppi abeliani localmente compatti (e totalmente disconnessi), gruppi abeliani polacchi (e non-archimedei), e spazi di Frechet su un campo munito di valutazione non-archimedea.
2022
21 Giugno
Francesco Sala (Università di Pisa)
Representations of cohomological Hall algebras of surfaces via torsion pairs
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The first part of the talk is devoted to a gentle introduction to the theory of cohomological Hall algebras (COHAs for brevity) of surfaces and their categorification. Moreover, their “quantum” nature will be discussed. In addition, the Dolbeaut cohomological Hall algebras of curves will be introduced. During the second part of the talk, I will address the problem of constructing pairs consisting of a COHA and a representation of it canonically associated to torsion pairs of the abelian category of coherent sheaves on a smooth projective complex surface S.
2022
21 Giugno
Angela Slavova
Mathematical modelling of nonlinear waves

seminario interdisciplinare

We study travelling wave solutions of shallow water waves. Camassa-Holm considered a third order nonlinear PDE of two variables modelling the propagation of unidirectional irrotational shallow water waves over a flat bed, as well as water waves moving over an underlying shear flow. In the special case of the motion of a shallow water over a flat bottom the corresponding system was simplified by Green and Naghdi and related to an appropriate two component first order Camassa-Holm system. Another interesting system of nonlinear PDE is the viscoelastic generalization of Burger's equation. In the above mentioned systems we look for travelling wave solutions and study their profiles. We use several results from the classical Analysis of ODE that enable us to give the geometrical picture and in several cases to express the solutions by the inverse of Legendre's elliptic functions. Moreover, we apply microlocal approach in studying the propagation of nonlinear waves. As an application, we present propagation of tsunami waves from their small disturbance at the sea level to the size they reach approaching the coast. Even with the aid of the most advanced computers it is not possible to find the exact solutions to the nonlinear governing equations for water waves. For this purpose we introduce Cellular Nonlinear Network (CNN) approach.
2022
17 Giugno
Mini-course on random behaviour of number-theoretical sequences, III

seminario di probabilità, sistemi dinamici

This mini-course will focus on recent advances on the statistical properties of certain number-theoretical sequences, seen as realizations of suitable stochastic processes. We will mainly focus on the distribution of square-free integers and their generalisations (e.g. k-free, B-free). We will discuss Sarnak’s conjecture on the disjointness of the Mobius function \mu(n) from sequences generated by zero-entropy dynamical systems. We will also prove that \mu^2(n) (the indicator of square-free integers) is completely deterministic and study the statistics of its patterns in long intervals.
2022
17 Giugno
Diego Moreira, Universidade Federal do Ceará (Fortaleza) Brasil
Up to the boundary gradient estimates in nonlinear free boundary problems with unbounded measurable ingredients

seminario di analisi matematica

In this talk, we discuss recent advances on up to the boundary gradient estimates for viscosity solutions of free boundary problems governed by fully nonlinear and quasilinear equations with unbounded coefficients. We present the new Inhomogeneous Pucci Barriers as new elements for the proof. If time permits, we discuss some of the main steps in the proof, namely, the trace estimate of the solution on the points of the fixed boundary that projects nontangentially over the free boundary. These methods are inspired by some ideas of Carlos Kenig in Harmonic Analysis.
2022
16 Giugno
Lorenzo Vecchi
Geometry and combinatorics behind KL polynomials of matroids

seminario di algebra e geometria

Since their first introduction in 1935, matroids have always been considered a great combinatorial tool for branches of applied mathematics like Coding Theory and Optimization. However, in the last years, a deep interplay between Matroid Theory, Algebraic Topology and Algebraic Geometry has been found: the Combinatorics of matroids allows us to fully describe the cohomology of some interesting varieties (the complement of an arrangement of hyperplanes, the wonderful model of De Concini-Procesi, the reciprocal plane); their Geometry led the way to solve long-standing combinatorial conjectures like the Heron-Rota-Welsh Conjecture and the Top-Heavy conjecture. In this talk, we will present Kazhdan-Lusztig polynomials for matroids, outlining the geometric setting in which they were first introduced in 2016. Many of their properties are still only conjectured, since their definition is given through an intricate recursion. We will show how one can partially solve these conjectures for wide classes of matroids using just combinatorial tools. This is a joint work with L. Ferroni and G.D. Nasr.
2022
16 Giugno
Cristian Gutierrez (Temple University)
Monotone mappings arising in optimal transport problems for non quadratic costs

seminario di analisi matematica

2022
15 Giugno
Jean Jacod
Systematic jump risk

seminario di probabilità

In a factor model for a large panel of N asset prices, a random time S is called a “systematic jump time” if it is not a jump time of any of the factors, but nevertheless is a jump time for a significant number of prices: one might for example think that those S’s are jump times of some hidden or unspecified factors. Our aim is to test whether such systematic jumps exist and, if they do, to estimate a suitably defined “aggregated measure” of their sizes. The setting is the usual high frequency setting with a finite time horizon T and observations of all prices and factors at the times iT/n for i = 0, . . . , n. We suppose that both n and N are large, and the asymptotic results (including feasible estimation of the above aggregated measure) are given when both go to infinity, without imposing restrictions on their relative size. In an empirical application, we document the existence of systematic jumps and further show that the associated risk commands a nontrivial risk premium.
2022
14 Giugno
Geometric interpretation of approximations of Nichols algebras
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Nichols algebras are graded Hopf algebras playing a prominent role in the study of pointed Hopf algebras and comprising symmetric algebras, exterior algebras and the positive part of quantized universal enveloping algebras. Kapranov and Schechtman have given a geometric interpretation of primitive bialgebras in terms of factorizable perverse sheaves. Through this equivalence, Nichols algebras correspond to IC complexes. In ongoing joint work in progress with Giovanna Carnovale and Lleonard Rubio y Degrassi, we give a geometric interpretation as well of approximations of Nichols algebras. This allows to reformulate geometrically various open problems on Nichols algebras.
2022
13 Giugno
Mini-course on random behaviour of number-theoretical sequences, II

seminario di probabilità, sistemi dinamici

This mini-course will focus on recent advances on the statistical properties of certain number-theoretical sequences, seen as realizations of suitable stochastic processes. We will mainly focus on the distribution of square-free integers and their generalisations (e.g. k-free, B-free). We will discuss Sarnak’s conjecture on the disjointness of the Mobius function \mu(n) from sequences generated by zero-entropy dynamical systems. We will also prove that \mu^2(n) (the indicator of square-free integers) is completely deterministic and study the statistics of its patterns in long intervals.
2022
07 Giugno
Marco Trevisiol (Sapienza Università di Roma)
Normality of Closures of Orthogonal Nilpotent Symmetric Orbits
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Kraft and Procesi showed that the Zariski closure of the conjugacy classes of type A are all normal and, in type B, C and D, they have described which ones are normal. In their work the Lie group acts on its Lie algebra by the adjoint action. In types B, C, D, a similar question can be asked for the action of the Lie group on the odd part of the general linear Lie algebra; that is the orthogonal group acting on the symmetric matrices and the symplectic group acting on the symmetric-symplectic matrices. Ohta showed that in the latter case every orbit has normal closures while this conclusion is not valid in the former case. In this talk I will present the main result of my Ph.D. thesis which gives a combinatorial description of the orbit whose closures are normal in the orthogonal case.
2022-06-07
Maria del Mar Gonzalez
Eigenfunctions for Levy Fokker-Planck equations

seminario di analisi matematica

When one writes the fractional heat equation in self-similar variables a drift term appears. We study the associated eigenvalue problem for this equation, which has a fractional Laplacian and a first order term under competition. Our main contribution is to give explicit Euclidean formulae of the fractional analogue of Hermite polynomials. A crucial tool is the Mellin transform, which is essentially the Fourier transform in logarithmic variable and which turns the gradient into multiplication. This is joint work with Hardy Chan, Marco Fontelos and Juncheng Wei.
2022-06-07
Michael Goldman
From local energy bounds to dimensional estimates in a reduced model for type-I superconductors

seminario di analisi matematica

In the limit of vanishing but moderate external magnetic field, we derived a few years ago together with S. Conti, F. Otto and S. Serfaty a branched transport problem from the full Ginzburg-Landau model. In this regime, the irrigated measure is the Lebesgue measure and, at least in a simplified 2d setting, it is possible to prove that the minimizer is a self-similar branching tree. In the regime of even smaller magnetic fields, a similar limit problem is expected but this time the irrigation of the Lebesgue measure is not imposed as a hard constraint but rather as a penalization. While an explicit computation of the minimizers seems here out of reach, I will present some ongoing project with G. De Philippis and B. Ruffini relating local energy bounds to dimensional estimates for the irrigated measure.
2022-06-07
Dario Mazzoleni
Singular analysis of the optimizers of the principal eigenvalue in weighted Neumann problems

seminario di analisi matematica

We study the minimization of the positive principal eigenvalue associated to a weighted Neumann problem settled in a bounded smooth domain \Omega\subset R^N, within a suitable class of sign-changing weights. This problem naturally arises in population dynamics. Denoting with u the optimal eigenfunction and with D its super-level set associated to the optimal weight, we perform the analysis of the singular limit of the optimal eigenvalue as the measure of D tends to zero. We show that, when the measure of D is sufficiently small, u has a unique local maximum point lying on the boundary of \Omega and D is connected. Furthermore, the boundary of D intersects the boundary of the box \Omega, and more precisely, ${\mathcal H}^{N-1}(\partial D \cap \partial \Omega)\ge C|D|^{(N-1)/N}$ for some universal constant C>0. Though widely expected, these properties are still unknown if the measure of D is arbitrary. This is a joint project with B. Pellacci and G. Verzini.
2022-06-07
Joaquim Serra
Fractional minimal surfaces: an invitation for the skeptics (and the convinced)

seminario di analisi matematica

Elliptic operators of fractional order were popularized, mainly thanks to Luis Caffarelli, during the early 2000's. Suddenly, we learnt that every classical PDE had a fractional counterpart (or even more than one in some cases!). Also, fractional versions of most important techniques and results in PDE were developed. In this context, the invention in the late 2000's of fractional minimal surfaces may not seem a very striking milestone. Over the years, however, the interest and depth of these new surfaces is becoming unquestionable, to the point that they may be a fundamental tool in order to better understand certain (famously delicate) questions on classical minimal surfaces, such as Yau's conjecture. In the talk I will describe some very recent works that, I hope, may help to convince a fraction of the remaining skeptics about the beauty and usefulness of nonlocal minimal surfaces.
2022-06-06
Nicolò Forcillo
Lipschitz regularity of almost minimizers for the p-Laplacian

seminario di analisi matematica

See pdf attached
2022-06-06
Paolo Baroni
New results for non-autonomous functionals with mild phase transition

seminario di analisi matematica

We describe how different regularity assumptions on the x-dependence of the energy impact the regularity of minimizers of some non-autonomous functionals having nonuniform ellipticity of moderate size. We put particular emphasis on double phase functionals with logarithmic phase transition, including some new results.
2022-06-06
Roberto Ognibene
A two-phase obstacle problem for the fractional Laplacian

seminario di analisi matematica

In this talk, I will consider a two-phase obstacle type problem driven by the fractional Laplacian and I will present some results concerning the local behavior of solutions and the regularity of their nodal set. Some time will be devoted to the description of the main tools, namely Almgren and Monneau type monotonicity formulas. This is a joint work with D. Danielli.
2022-06-06
Maria Medina
From sign-changing solutions of the Yamabe equation to critical competitive systems

seminario di analisi matematica

In this talk we will analyze the existence and the structure of different sign-changing solutions to the Yamabe equation in the whole space and we will use them to find positive solutions to critical competitive systems in dimension 4.
2022-06-06
Aldo Pratelli
On a weighted Cheeger problem

seminario di analisi matematica

In this talk we will discuss the Cheeger problem in a weighted domain. In particular, we are interested in the distribution of mass which maximizes the Cheeger constant in a ball (the minimization is always trivial). We will give some results, and notice how they depend on the bounds that we impose on the distribution. Joint work with Leonardi and Saracco.
06/06/2022
09/06/2022
Giacomo Lucertini
Optimal regularity for degenerate Kolmogorov equations with rough coefficients

seminario di analisi matematica, probabilità

We consider a class of degenerate equations satisfying a parabolic Hörmander condition, with coefficients that are measurable in time and Hölder continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal Hölder regularity, as well as Gaussian estimates. These results are key to study the backward Kolmogorov equations associated to a class of Langevin-type diffusions.
2022
03 Giugno
Aline Zanardini
Moduli of rational elliptic surfaces of index two
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Elliptic surfaces are ubiquitous in Mathematics. Examples include Enriques surfaces, Dolgachev surfaces, all surfaces of Kodaira dimension one, and many rational surfaces. In this talk we will focus on the latter. It is a classical result that all rational elliptic surfaces can be realized as a nine-fold blow-up of the plane, where the nine points (possibly infinitely near) are the base points of a pencil of plane curves of degree 3m, each of multiplicity m. The number m is called the index of the fibration. In joint work with Rick Miranda we have constructed a moduli space for rational elliptic surfaces of index two as a toric GIT quotient. The goal of my talk will be to explain our construction.
2022
01 Giugno
Mini-course on random behaviour of number-theoretical sequences, I

seminario di probabilità, sistemi dinamici

This mini-course will focus on recent advances on the statistical properties of certain number-theoretical sequences, seen as realizations of suitable stochastic processes. We will mainly focus on the distribution of square-free integers and their generalisations (e.g. k-free, B-free). We will discuss Sarnak’s conjecture on the disjointness of the Mobius function \mu(n) from sequences generated by zero-entropy dynamical systems. We will also prove that \mu^2(n) (the indicator of square-free integers) is completely deterministic and study the statistics of its patterns in long intervals.
2022
31 Maggio
Stavroula Makri
Surface braid groups and the splitting problem of the mixed braid groups of the projective plane
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The aim of this talk is to give an introduction to the surface braid groups and to present both the splitting problem of surface braid groups and certain results about this problem, concerning the mixed braid groups of the real projective plane. Surface braid groups are a generalisation, to any connected surface, of both the fundamental group of a surface and the braid groups of the plane, which are known as Artin braid groups and were defined by Artin in 1925. Surface braid groups were initially introduced by Zariski and then, during the 1960’s, Fox gave an equivalent definition from a topological point of view. In the first part of the talk, we will define the surface braid groups from both a geometric and a topological point of view and we will present their close relation to the symmetric groups. Moreover, we will present an important family of surface braid groups, the so-called mixed braid groups. Finally, we will describe the splitting problem of surface braid groups, which we will see in detail in the second part of the talk. In the second part of the talk, we will focus on the splitting problem, which, during the 1960’s, the period of the development of the theory of surface braid groups, was studied by many mathematicians; notably by Fadell, Neuwirth, Van Buskirk and Birman, and more recently by Gonçalves–Guaschi and Chen–Salter. In particular, we will focus on the case of the projective plane: we will present its braid groups as well as certain results that we obtained concerning the splitting problem of its mixed braid groups.
2022
31 Maggio
Margherita Lelli Chiesa
Irreducibility of Severi varieties on K3 surfaces
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Let (S,L) be a general K3 surface of genus g. I will prove that the closure in |L| of the Severi variety parametrizing curves in |L| of geometric genus h is connected for h>=1 and irreducible for h>=4, as predicted by a well known conjecture. This is joint work with Andrea Bruno.
2022
30 Maggio
Alessandro D'Andrea
A differential geometric description of exceptional projective irreducible (discrete) representations of the Hamiltonian Lie algebra of Cartan type
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Some exact complexes of irreducible discrete representations of the unique irreducible central extension of H_n have only been constructed by hand. I will provide a differential geometric description by using base change in the pseudoalgebra language.
2022
27 Maggio
Marco Moraschini
Introduzione alla coomologia limitata, parte 2
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

La coomologia limitata è una variante analitico-funzionale della classica coomologia ed è stata introdotta da Johnson e Trauber nel contesto delle algebre di Banach all’inizio degli anni ’70. Successivamente, Gromov ha esteso lo studio della coomologia limitata dai gruppi agli spazi (1982). A seguito del lavoro pionieristico di Gromov la coomologia limitata (per gruppi e per spazi) si è sviluppa sempre di più come filone di ricerca indipendente con svariate applicazioni alla geometria in bassa dimensione e alla teoria geometrica dei gruppi. In questo seminario introdurremo la nozione di coomologia limitata e vedremo come nel caso di gruppi amenabili si annulli (in grado positivo). Al contrario, studieremo il suo comportamento in presenza di gruppi iperbolici, e.g. nel caso di gruppi liberi non abeliani. A seconda del tempo rimanente discuteremo eventuali applicazioni della coomologia limitata alla topologia delle varietà, con particolare attenzione alla sua relazione con il volume simpliciale (un invariante omotopico di varietà introdotto da Gromov nel 1982).
2022
26 Maggio
Tobias Weth
The fractional Poisson problem and the logarithmic Laplacian

seminario di analisi matematica

I will discuss some recent results on the family of fractional Poisson problems $(-\Delta)^s u =f$ in $\Omega$, $u=0$ on $\Omega^c$ of order $2s$ and its connection to the logarithmic Laplacian operator. This connection allows, in particular, to characterize the $s$-dependence of solutions to this family. Special attention will be given to the case $f\equiv 1$, i.e., the fractional torsion problem. This is joint work with Sven Jarohs and Alberto Saldana.
2022
26 Maggio
Simona Manzone
Come scrivere un CV

seminario interdisciplinare

Il seminario, rivolto agli studenti della magistrale, è diviso in due parti: nella prima verrà fatta un’introduzione generale sul Curriculum Vitae (CV), spiegando a cosa serve e come deve essere strutturato. Particolare attenzione verrà data al CV per l’ambito accademico. Nella seconda parte sarà trattato il CV per il mondo del lavoro e l’utilizzo del social network LinkedIn per entrare nel mercato del lavoro. Calendario dell’evento *Prima parte: *martedì 24 maggio h 9:00 Aula Tonelli, Dott. Roberto Pagaria. *Seconda parte:* giovedì 26 maggio h 9:00 Aula Vitali, HR manager Simona Manzone. https://corsi.unibo.it/magistrale/matematica/bacheca/come-scrivere-un-cv
2022
25 Maggio
Mario De Caro
Tempo e coscienza tra filosofia morale e neuroscienze
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
25 Maggio
Pietro Pietrini
TEMPO, COSCIENZA E SCIENZE COGNITIVE
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
25 Maggio
Balconi Michela
Tempo, coscienza e scienze cognitive
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
24 Maggio
The Jacobi theta function near the real line

seminario di algebra e geometria, analisi matematica, sistemi dinamici

The Jacobi elliptic theta function is a function of two complex variables, \tau (with positive imaginary part) and z. As \tau approaches the real line, the function may blow up. In a joint work with Tariq Osman (Queen’s University), we find a uniform bound for generalised Weyl sums using homogeneous dynamics. As a consequence, we find affine curves z=z(\tau) along which the blow up in the Jacobi theta function can be uniformly controlled.
2022
24 Maggio
Leone Slavich (Università di Pavia)
Totally geodesic immersions of hyperbolic manifolds
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The study of totally geodesic immersions between (complete, finite-volume) hyperbolic manifolds is a classical problem in the field of hyperbolic geometry. There are two main approaches to this problem which often interplay with each other: 1) Given a hyperbolic manifold N, determine the hyperbolic manifolds in which N can be immersed geodesically; 2) Given a hyperbolic manifold, determine its totally geodesic immersed submanifolds. We will show how it is possible to build totally geodesic immersed submanifolds in a hyperbolic manifold M using finite subgroups in the commensurator of M. We will then focus on the class of arithmetic manifolds i.e. those whose fundamental groups is commensurable with the integral points of some k-form of Isom(H^n)=PO(n,1,R), for some real algebraic number field k. We will show how to characterise all totally geodesic immersions in this setting through the analysis of Vinberg's commensurability invariants: the adjoint trace field (which is an algebraic number field) and the ambient group (an algebraic group defined over the adjoint trace field). This is joint work with Mikhail Belolipetski, Nikolay Bogachev and Alexander Kolpakov.
2022
24 Maggio
Stability conditions on stacks, IV

seminario di algebra e geometria

Mini-corso di Dottorato, Lezione IV Many geometric structures on algebraic varieties (such as vector bundles or coherent sheaves) are best studied by considering the collection of all such structures, modulo some natural equivalence, and giving it a geometric structure itself. Depending on the moduli problem considered, this may lead to a moduli scheme, a moduli space, or a moduli stack. Focusing on examples related to vector bundles on smooth curves, we will discuss the geometry of the corresponding moduli spaces and stacks, explaining how the notion of stability throws a bridge from stacks to spaces. This will be preceded by some relevant background (though very informal and example-driven) on stacks and on geometric invariant theory.
2022
23 Maggio
Stability conditions on stacks, III

seminario di algebra e geometria

Mini-Corsi di Dottorato, Lezione III Many geometric structures on algebraic varieties (such as vector bundles or coherent sheaves) are best studied by considering the collection of all such structures, modulo some natural equivalence, and giving it a geometric structure itself. Depending on the moduli problem considered, this may lead to a moduli scheme, a moduli space, or a moduli stack. Focusing on examples related to vector bundles on smooth curves, we will discuss the geometry of the corresponding moduli spaces and stacks, explaining how the notion of stability throws a bridge from stacks to spaces. This will be preceded by some relevant background (though very informal and example-driven) on stacks and on geometric invariant theory.
2022
20 Maggio
Gianluca Giacchi
Eardrums writing scores: time-frequency analysis, the handbook of absolute pitches

seminario di analisi matematica

A score contains all the information needed to reproduce a music signal in time: the octaves representing different frequency intervals. Time-frequency analysis is a branch of harmonic analysis that studies the relations between tempered distributions and their Fourier transforms that, in this context, precisely represent the amplitude of a signal in time and the amplitude of its frequencies. This seminar aims to provide a brief introduction on several aspects of time-frequency analysis: from uncertainty principles, mathematical results providing hindrances to the exact localization of signals, to pseudodifferential operators, whose study fits surprisingly and naturally into a time-frequency analysis setting.
2022
20 Maggio
Marco Moraschini
Introduzione alla coomologia limitata
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

La coomologia limitata è una variante analitico-funzionale della classica coomologia ed è stata introdotta da Johnson e Trauber nel contesto delle algebre di Banach all’inizio degli anni ’70. Successivamente, Gromov ha esteso lo studio della coomologia limitata dai gruppi agli spazi (1982). A seguito del lavoro pionieristico di Gromov la coomologia limitata (per gruppi e per spazi) si è sviluppa sempre di più come filone di ricerca indipendente con svariate applicazioni alla geometria in bassa dimensione e alla teoria geometrica dei gruppi. In questo seminario introdurremo la nozione di coomologia limitata e vedremo come nel caso di gruppi amenabili si annulli (in grado positivo). Al contrario, studieremo il suo comportamento in presenza di gruppi iperbolici, e.g. nel caso di gruppi liberi non abeliani. A seconda del tempo rimanente discuteremo eventuali applicazioni della coomologia limitata alla topologia delle varietà, con particolare attenzione alla sua relazione con il volume simpliciale (un invariante omotopico di varietà introdotto da Gromov nel 1982).
2022
20 Maggio
Stability conditions on stacks, II

seminario di algebra e geometria

Mini Corso di Dottorato: Lezione II Many geometric structures on algebraic varieties (such as vector bundles or coherent sheaves) are best studied by considering the collection of all such structures, modulo some natural equivalence, and giving it a geometric structure itself. Depending on the moduli problem considered, this may lead to a moduli scheme, a moduli space, or a moduli stack. Focusing on examples related to vector bundles on smooth curves, we will discuss the geometry of the corresponding moduli spaces and stacks, explaining how the notion of stability throws a bridge from stacks to spaces. This will be preceded by some relevant background (though very informal and example-driven) on stacks and on geometric invariant theory.
2022
19 Maggio
Bruno Franchi
Teoria Geometrica della Misura nei gruppi di Carnot e sottovarietà intrinseche (Geometric Measure Theory in Carnot groups and intrinsic submanifolds).

seminario di analisi matematica

Carnot groups provide the simplest instance of metric spaces that are non-Riemannian but are still endowed with a rich structure of dilations and translations, making possible to develop a non-Riemannian Geometric Measure Theory. The first step of this program consists in the search of a good (i.e natural) notion of regular submanifolds and in the study of their properties. In this talk we present few chapters of this program along the guidelines of a joint monograph with Raul Serapioni and Francesco Serra Cassano, Some topics of Geometric Measure Theory in Carnot Groups (in preparation). - I gruppi di Carnot forniscono l'esempio più semplice di spazi metrici che non sono riemanniani ma che sono comunque dotati di una ricca struttura di dilatazioni e traslazioni che permettono di sviluppare una Teoria geometrica della misura non riemanniana. Il primo passo di questo programma consiste nella ricerca di una buona (cioè naturale) nozione. di sottovarietà regolari e nello studio delle loro proprietà. In questo seminario presentiamo alcuni capitoli di questo programma secondo le linee di una monografia scritta in collaborazione con Raul Serapioni e Francesco Serra Cassano, Some topics of Geometric Measure Theory in Carnot Groups (in preparazione).
2022
19 Maggio
Stability conditions on stacks, I

seminario di algebra e geometria

Lezione I, Minicorso di Dottorato. Many geometric structures on algebraic varieties (such as vector bundles or coherent sheaves) are best studied by considering the collection of all such structures, modulo some natural equivalence, and giving it a geometric structure itself. Depending on the moduli problem considered, this may lead to a moduli scheme, a moduli space, or a moduli stack. Focusing on examples related to vector bundles on smooth curves, we will discuss the geometry of the corresponding moduli spaces and stacks, explaining how the notion of stability throws a bridge from stacks to spaces. This will be preceded by some relevant background (though very informal and example-driven) on stacks and on geometric invariant theory.
2022
19 Maggio
Stacks, Stability conditions.
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022
Many geometric structures on algebraic varieties are best studied by considering the collection of structures, modulo some natural equivalence, and giving it a geometric structure itself. We will a gentle introduction, focused on examples. Stesso link per il Seminario del Prof. M. Thaddeus, stessa ora
2022
10 Maggio
Simone Diverio
Sviluppi recenti sulla congettura di Lang: quozienti di domini limitati
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

La congettura di Lang (1986) caratterizza le varietà complesse proiettive (o, più generalmente, Kähler compatte) iperboliche nel senso di Kobayashi come quelle di tipo generale assieme a tutte le loro sottovarietà. Lungi dall’essere dimostrata al momento, la congettura è però nota in una serie di casi paradigmatici ancorché particolari. Ci concentreremo in particolare su una direzione della congettura, spiegando come sia possibile verificare ad esempio che un quoziente libero e compatto di un dominio limitato dello spazio affine complesso abbia tutte sottovarietà di tipo generale (lavoro in collaborazione con S. Boucksom). Tempo permettendo, descriveremo alcune variazioni sul tema, considerando tipi di quozienti più generali: non più necessariamente lisci, né compatti (lavoro in collaborazione con B. Cadorel e H. Guenancia).
2022
10 Maggio
Valeria Simoncini
Matrix equations: from theory to (computational) practice
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022

seminario di analisi numerica

The numerical solution of possibly large dimensional algebraic linear systems permeates scientific modelling. Often systems with multiple right-hand sides arise, whose efficient numerical solution usually requires ad-hoc procedures. In the past decades a new class of linear equations has shown to be the natural algebraic framework in the discretization of mathematical models in a variety of scientific applications. These problems are given by multiterm linear matrix equations of the form A_1 X B_1 + A_2 X B_2 + ... + A_k X B_k = C where all appearing terms are matrices of conforming dimensions, and X is an unknown matrix. The case k=2 is called the Sylvester equation, and computational methods for its solution are well established, especially for small dimensions. The general multiterm case turns out to be a key ingredient in problems such as time-space, stochastic and parametric partial differential equations. Its numerical solution is the current challenge, though little is known also about its algebraic properties. In this lecture we give a gentle introduction to the problem, and discuss various attempts to numerically solve it.
2022
09 Maggio
Alessandro D'Andrea
Moltiplicazione, numeri primi ed errori fortunati
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Parlerò di come affrontare due problemi familiari (moltiplicare numeri interi e stabilire se un numero sia primo) in modo insolito e di quali ricadute questo abbia al di fuori della matematica.
2022
06 Maggio
Stefano Francaviglia
Introduzione all'outer space, parte 2
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

2022
06 Maggio
Aldo Conca
Resolution of Ideals Associated to Subspace Arrangements
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The ideal of definition of a linear subspace in a projective space has a very simple structure and hence a very simple free resolution, i.e. a Koszul complex. What can we say for the ideal that defines a finite collection of linear subspaces, subspace arrangements, in a projective space? Here we can take the intersection of the ideals defining the individual subspaces or their product. For the intersection, the structure of the resolution remains largely mysterious. For the product instead the resolution can be described and it turns out that it is supported on a polymatroid associated with the subspace arrangement. Joint work with Manolis Tsakiris (Chinese Academy of Sciences). arXiv:1910.01955v2
2022
05 Maggio
Limiting distributions of quadratic Weyl sums and their generalisations, part II

seminario di fisica matematica, probabilità, sistemi dinamici, interdisciplinare

I will discuss the limiting distribution of quadratic Weyl sums and their generalisations (e.g. classical Jacobi theta functions). Quadratic Weyl sums are a special kind of exponential sums that appear naturally in number theory, mathematical physics, and representation theory. They can be interpreted as deterministic walks (with a random ‘seed’) in the complex plane. Generalising Sarnak’s equidistribution of horocycles under the action of the geodesic flow, one can study the limiting distribution of such Weyl sums. A stochastic process of number-theoretical origin can be defined using such sums. ------- Seminario nell'ambito del corso di dottorato "Randomness in Number Theory: dynamical and probabilistic methods”, tenuto dal Prof. Cellarosi per il Dottorato in Matematica Unibo
2022
03 Maggio
Limiting distributions of quadratic Weyl sums and their generalisations, part I

seminario di fisica matematica, interdisciplinare, probabilità, sistemi dinamici

I will discuss the limiting distribution of quadratic Weyl sums and their generalisations (e.g. classical Jacobi theta functions). Quadratic Weyl sums are a special kind of exponential sums that appear naturally in number theory, mathematical physics, and representation theory. They can be interpreted as deterministic walks (with a random ‘seed’) in the complex plane. Generalising Sarnak’s equidistribution of horocycles under the action of the geodesic flow, one can study the limiting distribution of such Weyl sums. A stochastic process of number-theoretical origin can be defined using such sums. ------- Seminario nell'ambito del corso di dottorato "Randomness in Number Theory: dynamical and probabilistic methods”, tenuto dal Prof. Cellarosi per il Dottorato in Matematica Unibo
2022
03 Maggio
Florestan Martin-Baillon
Bifurcation currents for families of group representations in higher rank
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Finitely generated groups acting on projective spaces are examples of holomorphic dynamical systems which exhibit a variety of different behaviours. We introduce the notion of proximal stability which measures a form of dynamical stability for the action of a holomorphic family of group representations and we will explain how this property can be detected using a bifurcation current on the parameter space of the family. This bifurcation current measure the pluriharmonicity of the top Lyapunov exponent of the family of representation, defined using a random walk on the group.
2022
02 Maggio
Lucio Russo
Una rivisitazione della misura di Eratostene. Breve ciclo di due seminari.

seminario di fisica matematica, interdisciplinare, storia della matematica

La misura di Eratostene della circonferenza terrestre, essendosi perduto il lavoro originale, è sempre riportata attribuendo a Eratostene le assunzioni semplificatrici fatte da Cleomede nel suo resoconto divulgativo. Si propone invece una ricostruzione del procedimento originale, basata anche su una stima dell’accuratezza del risultato ottenuta con metodi statistici.
2022
29 Aprile
Stefano Francaviglia
Outer space
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

Cos'è e a cosa serve l'Outer Space.
2022
28 Aprile
Thomas Lam
Grassmannians and statistical mechanical models, 3

seminario di algebra e geometria, fisica matematica, interdisciplinare

2022
27 Aprile
Thomas Lam
Grassmannians and statistical mechanical models, 2

seminario di algebra e geometria, fisica matematica, interdisciplinare

2022
26 Aprile
Thomas Lam
Grassmannians and statistical mechanical models, 1

seminario di algebra e geometria, fisica matematica, interdisciplinare

2022
26 Aprile
Irina Mitrea (Department of Mathematics, Temple University)
A Sharp Divergence Theory with Non-Tangential Traces

seminario di analisi matematica

The Integration by Parts Formula, which is equivalent with the Divergence Theorem, is one of the most basic tools in Analysis. Originating in the works of Gauss, Ostrogradsky, and Stokes, the search for an optimal version of this fundamental result continues through this day and these efforts have been the driving force in shaping up entire subbranches of mathematics, like Geometric Measure Theory. In this talk I will review some of these developments (starting from elementary considerations to more sophisticated versions) and I will discuss recents result regarding a sharp divergence theorem with non-tangential traces. This is joint work with D. Mitrea and M. Mitrea.
2022
26 Aprile
Martina Lanini
Symmetric quivers and symmetric varieties
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

In this talk I will report on ongoing joint work with Ryan Kinser and Jenna Rajchgot, on varieties of symmetric quiver representations. These varieties are acted upon by a reductive group via change of basis, and it is natural to ask for a parametrisation of the orbits, for the closure inclusion relation among them, for information about the singularities arising in orbit closures. Since the Eigthies, same (and further) questions about representation varieties for type A quivers have been attached by relating such varieties to Schubert varieties in type A flag varieties (Zelevinsky, Bobinski-Zwara, ...). I will explain that in the symmetric setting it is possible to interpret the above questions in terms of certain symmetric varieties. For example, we show that singularities of an orbit closure of a symmetric quiver representation variety are smoothly equivalent to singularities of an appropriate Borel orbit closure on a symmetric variety. As a consequence, we obtain an infinite class of symmetric quiver loci that are normal and Cohen-Macaulay.
2022
21 Aprile
Gilberto Bini
Fibrati vettoriali big
nel ciclo di seminari: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Dopo aver richiamato alcune nozioni sui fibrati lineari big, si parlerà di fibrati vettoriali big sia su superfici K3 sia sul loro schema di Hilbert di punti. In particolare, verranno descritte alcune famiglie di fibrati big, stabili e globalmente generati.
2022
21 Aprile
Margherita Porcelli
TOC4Deep - first online-onsite workshop
nell'ambito della serie: SEMINARI MAT/08 TEAM

seminario di analisi numerica

As part of the Una Europa funded grant TOC4Deep (Tensor-based Optimal Control Approaches for Deep Learning) a series of half-day workshops will be held over the next 6 months to encourage scientific networking and discussions between the project universities of Edinburgh, Bologna and KU Leuven. The first of these workshops will take place on Thursday 21st April, with a focus on research relating to optimization and optimal control. The workshop will be hybrid, with in person attendance in JCMB 5323 or via Zoom (link to follow). The timetable and speaker information is below: Time (BST) - please mind the time zone 9-9.30 - Introduction/TOC4Deep presentation 9.30-10.15 - John Pearson, University of Edinburgh "Preconditioned Iterative Methods for Multiple Saddle-point Systems Arising from PDE-constrained Optimization" 10.15-10.30 - Break 10.30-11.15 - Wim Michiels, KU Leuven "Stability, Robustness Analysis and Model Order Reduction of Periodic Control Systems with Delay" 11.15-12 - Margherita Porcelli, Università di Bologna "A spectral PALM algorithm for Dictionary Learning"
2022
14 Aprile
Ermanno Lanconelli
Sorgenti di un calcolo infinitesimale privo d’infinitesimi. Fermat senza “fantasmi” I
Il calcolo infinitesimale, “uno dei successi teorici più elevati della conoscenza”, in origine era fondato su una nozione euristica, rimasta per lungo tempo imprecisata e controversa: quella di infinitesimo. Celebre il sarcastico giudizio di George Berkeley - vescovo e filosofo irlandese del XVIII secolo - per il quale gli infinitesimi altro non sono che ''fantasmi di quantità scomparse''. Di quei fantasmi il calcolo infinitesimale potè liberarsi soltanto cent'anni dopo la nascita, con l'aritmetizzazione dell'analisi intrapresa da Karl Weierstrass e fondata sulla nozione di limite. Ma, come tutte le grandi conquiste, anche quella del limite ebbe - come ha tuttora - un prezzo da pagare, dovuto al complesso bagaglio insiemistico-topologico che quel concetto porta con sé. Una via più agevole di quella seguita da Weierstarss si scopre risalendo alle sorgenti del calcolo infinitesimale e a una delle sue idee fondanti, quella contenuta nel metodo di Fermat per la determinazione dei massimi e dei minimi delle funzioni reali di variabile reale: si scopre precisamente l'esistenza di due notevoli classi di funzioni, quella dei polinomi e quella delle funzioni convesse, che il calcolo infinitesimale lo portano nei genomi, un calcolo che non richiede infinitesimi né limiti, del tutto libero da ''fantasmi''. Da questo naturale calcolo differenziale nasce una proposta didattica nuova, che antepone la rigorosa definizione di derivata a quella di limite. Il corso è incentrato su questa nuova proposta didattica per l’insegnamento dell’analisi matematica nel triennio della scuola superiore, che è presentata nel libro C. Facchini - E. Lanconelli “Un cammino tra massimi e minimi: ciottoli e sorgive del calcolo infinitesimale”, Pitagora Editrice, Bologna 2021.
2022
13 Aprile
Alessandro Sarti
L'emergenza semiolinguistica
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
12 Aprile
Ludovico Battista
Hyperbolic 4-Manifolds with perfect circle-valued Morse functions
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

In dimension 3, combining the study of the geometry and the topology of manifolds led to interesting and surprising results. The generalization of such a connection in dimension 4 seems to be a promising approach to better understand this complicated world. An intriguing 3-dimensional phenomenon is the existence of hyperbolic manifolds which fiber over the circle. Such manifolds cannot exist in dimension 4, due to a constraint given by Euler Characteristic and the Gauss - Bonnet formula. We will introduce the notion of "perfect circle-valued Morse function", which appears to be the natural generalization of "fibration over S^1", and we will introduce some tools to build a hyperbolic 4-manifold that admits such a function. To do this we will elaborate on a paper of Jankiewicz - Norin - Wise that makes use of Bestvina - Brady theory. Joint work with Bruno Martelli.
2022
12 Aprile
Elisa Affili
Controllability in Lotka-Volterra competitive systems with positive controls

seminario di analisi matematica

Ecology models describing the evolution of population densities, as Lotka-Volterra competitive systems, require the solutions to be positive and bounded. Hence, the boundary controls have also to satisfy some constraints, so classic techniques in control theory cannot be applied. In this talk, we will describe non-controllability phenomena due to the presence of barrier solutions depending on the parameters of the systems. This is joint work with Enrique Zuazua.
2022
11 Aprile
Möbius randomness, probability, and dynamics

seminario interdisciplinare

The Möbius function \mu plays a central role in Number Theory. If n is not square-free (i.e. it is divisible by the square of some prime), then \mu(n)=0 otherwise \mu(n) equals +1 or -1 depending on the parity of the number of prime divisors of n. The average behaviour of this function can be understood by considering its partial sums. The problem of estimating the growth of such sums can be can easy (equivalent to the Prime Number Theorem) or very hard (equivalent to the Riemann Hypothesis), depending on the precision we require. Understanding the randomness’ of the Möbius function can done by studying its autocorrelations (conjectured to be all zero by Chowla in 1965) or its correlations with other sequences. In 2010 Sarnak conjectured that the Möbius function should not correlate with any sequence of low complexity, i.e. sequences generated by dynamical systems with zero topological entropy. We will discuss what is known about Chowla’s and Sarnak’s conjectures and some of their weaker forms. We can ask to what extent the Möbius function behaves like a sequence of random variables with values in {0,+1,-1}, but we cannot hope for independence. In fact, when we study the simpler sequence \mu^2 (which is the indicator of the set of square-free integers) we see that it highly self-correlated. It can be shown, in fact, that \mu^2 is a typical realization of a stochastic process with as little randomness as possible. The approach we take in the study of such problem is dynamical, which has proven very fruitful. Time permitting, we will also survey some very recent results on the statistics of square-free integers in short intervals, where randomness re-appears.
2022
11 Aprile
Emanuele Ventura
Singular vector tuples of tensors and Kalman varieties

seminario di algebra e geometria

Kalman varieties of tensors are algebraic varieties consisting of tensors whose singular vector tuples lay on prescribed subvarieties. They were first studied by Ottaviani and Sturmfels in the context of matrices. I will talk about some families of Kalman varieties, extending previous work of Ottaviani and Shahidi to the partially symmetric context, highlighting the special role of isotropic vectors in the spectral theory of tensors. I will indicate how to describe the totally isotropic Kalman variety as a dual variety and how to obtain a generating function whose coefficients are the degrees of these varieties. This is based on a joint work with Shahidi and Sodomaco.
2022
08 Aprile
Marco Moraschini
Cenni di teoria geometrica dei gruppi
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

[Italiano] In questo seminario daremo una breve introduzione alla teoria geometria dei gruppi, con particolare attenzione all’interazione fra topologia/geometria e algebra. Ci concentreremo principalmente sui gruppi amenabili e sui gruppi liberi non abeliani. [English] In this talk we will give a quick overview on geometric group theory with special emphasis on the interactions between topology, algebra and geometry. We will mainly focus our attention on amenable groups and non-abelian free groups.
2022
08 Aprile
Ermanno Lanconelli
Sorgenti di un calcolo infinitesimale privo d’infinitesimi. Fermat senza “fantasmi” I
Il calcolo infinitesimale, “uno dei successi teorici più elevati della conoscenza”, in origine era fondato su una nozione euristica, rimasta per lungo tempo imprecisata e controversa: quella di infinitesimo. Celebre il sarcastico giudizio di George Berkeley - vescovo e filosofo irlandese del XVIII secolo - per il quale gli infinitesimi altro non sono che ''fantasmi di quantità scomparse''. Di quei fantasmi il calcolo infinitesimale potè liberarsi soltanto cent'anni dopo la nascita, con l'aritmetizzazione dell'analisi intrapresa da Karl Weierstrass e fondata sulla nozione di limite. Ma, come tutte le grandi conquiste, anche quella del limite ebbe - come ha tuttora - un prezzo da pagare, dovuto al complesso bagaglio insiemistico-topologico che quel concetto porta con sé. Una via più agevole di quella seguita da Weierstarss si scopre risalendo alle sorgenti del calcolo infinitesimale e a una delle sue idee fondanti, quella contenuta nel metodo di Fermat per la determinazione dei massimi e dei minimi delle funzioni reali di variabile reale: si scopre precisamente l'esistenza di due notevoli classi di funzioni, quella dei polinomi e quella delle funzioni convesse, che il calcolo infinitesimale lo portano nei genomi, un calcolo che non richiede infinitesimi né limiti, del tutto libero da ''fantasmi''. Da questo naturale calcolo differenziale nasce una proposta didattica nuova, che antepone la rigorosa definizione di derivata a quella di limite. Il corso è incentrato su questa nuova proposta didattica per l’insegnamento dell’analisi matematica nel triennio della scuola superiore, che è presentata nel libro C. Facchini - E. Lanconelli “Un cammino tra massimi e minimi: ciottoli e sorgive del calcolo infinitesimale”, Pitagora Editrice, Bologna 2021.
2022
07 Aprile
Federica Sani (Università di Modena e Reggio Emilia).
Extremal functions for Adams inequalities with Navier boundary conditions

seminario di analisi matematica

We prove the existence of extremal functions for second order Adams inequalities with Navier boundary conditions on balls in R^n in any dimension n>3. The proof is based on a symmetrization argument and the ideas introduced by Carleson and Chang to prove the existence of extremal functions in the first order case, i.e. extremal functions for the Trudinger-Moser inequality on balls. We also derive a supercritical version of this result for spherically symmetric functions.
2022
06 Aprile
Alessandro Calvia
On a class of partially observed systems arising in singular optimal control

seminario di probabilità

2022
06 Aprile
Allen Knutson
Stratified spaces and degenerations

seminario di algebra e geometria

This mini-course will tie together several topics, in approximately the following order. Very little background will be assumed, essentially basic commutative algebra, though exposure to Gröbner bases would probably be a bonus. 1. Schubert varieties, matrix Schubert varieties, and pipe dreams 2. Frobenius splitting, Kazhdan-Lusztig varieties, and quiver cycles 3. Positroid varieties, Bruhat atlases, and wonderful compactifications of group
2022
05 Aprile
Michele Graffeo (SISSA)
On the Behrend function and the blowup of some fat points
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Not much is known about the geometric properties of the punctual Hilbert scheme of fat points of length n supported at the origin of the affine plane A^2. In order to investigate them, a huge number of invariants, for fat points, has been introduced (e.g. multiplicity, order, type, blowup tree...). I will focus on the Behrend number v_Z of a fat point Z in A^2. Such invariant can be defined in terms of the blowup of the affine plane with center the subscheme Z. I will discuss the problem of computing the Behrend number of a monomial fat point following a joint work with Andrea T. Ricolfi. In particular, I will explain, first in the normal setting, how toric geometry methods apply in the construction of the blowup and in the computation of v_Z. Then, I will move to the non-normal setting, and I will show some examples of computation. Finally, if time permits, I will show some difficulties that arise in higher dimension.
2022
05 Aprile
Allen Knutson
Schubert Calculus

seminario di algebra e geometria

2022
05 Aprile
Allen Knutson (Cornell University)
Schubert calculus and quiver varieties
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Since the 1970s we have known that the structure constants for intersection theory on compact complex homogeneous spaces (such as Grassmannians) are nonnegative, but our only formulae for these constants (outside special cases) are essentially as alternating sums. The most effective tool to date for giving manifestly positive formulae are the "puzzles" that Terry Tao and I introduced, but the connection to quantum integrable systems observed by Paul Zinn-Justin made it clear that the puzzles should be solving a richer problem. This turns out to involve Nakajima quiver varieties, and has shed light even on the original problem of intersecting three cells in a Grassmannian. This work is joint with Paul Zinn-Justin.
2022
04 Aprile
Allen Knutson
The mathematics of juggling

seminario di algebra e geometria, didattica della matematica, interdisciplinare

Around 1985 three groups of jugglers hit upon the same mathematization of juggling patterns. I'll explain (and demonstrate) this system, connect it to natural questions in linear algebra, and to some recently studied probabilistic models.
2022
01 Aprile
Ludovico Battista
Funzioni di Morse Perfette a valori in S^1 su 4-varietà iperboliche (parte 2)
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

Lo studio delle varietà iperboliche e delle loro proprietà topologiche ha avuto un forte impatto nello studio delle varietà in dimensione bassa. La connessione tra la topologia di una varietà e il tipo di metrica che essa supporta ha portato al celebratissimo Teorema di Geometrizzazione in dimensione 3. In questa dimensione, le varietà iperboliche sono ampiamente le più complesse e le più studiate tra quelle che ammettono una geometria. In dimensione più alta la prominenza del ruolo delle varietà iperboliche è meno chiara. Non sembra però essere meno interessante chiedersi quali siano le proprietà topologiche che una 4-varietà iperbolica può avere. In questo seminario (e nel prossimo) daremo la definizione di funzione di Morse perfetta a valori in S^1 (in breve, PCVMF), e spiegheremo perché è interessante cercare varietà che ammettano una tale funzione. Richiameremo la costruzione di una varietà iperbolica mediante colorazione di politopi, e daremo un'idea di come sia possibile utilizzare questa struttura per costruire una PCVMF su una 4-varietà iperbolica.
2022
01 Aprile
Ermanno Lanconelli
Sorgenti di un calcolo infinitesimale privo d’infinitesimi. Fermat senza “fantasmi” I
Il calcolo infinitesimale, “uno dei successi teorici più elevati della conoscenza”, in origine era fondato su una nozione euristica, rimasta per lungo tempo imprecisata e controversa: quella di infinitesimo. Celebre il sarcastico giudizio di George Berkeley - vescovo e filosofo irlandese del XVIII secolo - per il quale gli infinitesimi altro non sono che ''fantasmi di quantità scomparse''. Di quei fantasmi il calcolo infinitesimale potè liberarsi soltanto cent'anni dopo la nascita, con l'aritmetizzazione dell'analisi intrapresa da Karl Weierstrass e fondata sulla nozione di limite. Ma, come tutte le grandi conquiste, anche quella del limite ebbe - come ha tuttora - un prezzo da pagare, dovuto al complesso bagaglio insiemistico-topologico che quel concetto porta con sé. Una via più agevole di quella seguita da Weierstarss si scopre risalendo alle sorgenti del calcolo infinitesimale e a una delle sue idee fondanti, quella contenuta nel metodo di Fermat per la determinazione dei massimi e dei minimi delle funzioni reali di variabile reale: si scopre precisamente l'esistenza di due notevoli classi di funzioni, quella dei polinomi e quella delle funzioni convesse, che il calcolo infinitesimale lo portano nei genomi, un calcolo che non richiede infinitesimi né limiti, del tutto libero da ''fantasmi''. Da questo naturale calcolo differenziale nasce una proposta didattica nuova, che antepone la rigorosa definizione di derivata a quella di limite. Il corso è incentrato su questa nuova proposta didattica per l’insegnamento dell’analisi matematica nel triennio della scuola superiore, che è presentata nel libro C. Facchini - E. Lanconelli “Un cammino tra massimi e minimi: ciottoli e sorgive del calcolo infinitesimale”, Pitagora Editrice, Bologna 2021.
2022
01 Aprile
Milena Zappoli - Head of technological innovation, IT systems evolution, data management and engagement proposals - Hera Group
Intelligenza artificiale applicata ai servizi ambientali

seminario interdisciplinare

2022
01 Aprile
Nicolas Perkowski
Introduction to singular SPDEs via paracontrolled distributions - Lecture IV

seminario di analisi matematica, probabilità

4th lecture: Beyond d=2: - paracontrolled distributions - the Phi 4-3 equation
2022
31 Marzo
Luca Migliorini
L’ubiquità della teoria di Hodge

seminario interdisciplinare

La teoria di Hodge, sviluppata tra gli altri da H. Weyl, K. Kodaira, W. Hodge, costituisce una delle più importanti interazioni tra l’analisi delle equazioni alle derivate parziali, in questo caso ellittiche lineari, e la geometria delle varietà. Nel caso di varietà Kähleriane, essa fornisce un insieme molto potente di informazioni di tipo topologico. Alcune tra le più sorprendenti applicazioni della teoria di Hodge sono in ambito combinatorio, e danno risultati di unimodalità o log-concavità per successioni di interi di origine combinatoria quali il vettore delle facce di un poliedro e alcuni invarianti di grafi. Tipicamente a una larga classe di questi oggetti combinatorici, che chiamiamo “realizzabili”, si riesce ad associare una varietà Kähleriana, e i risultati base della teoria di Hodge di questa varietà si traducono in enunciati combinatorici di notevole rilevanza. Negli ultimi anni, soprattuto ad opera di J. Huh, K. Adiprasito, B.Wang, E. Katz, si è visto che sorprendentemente i risultati della teoria di Hodge valgono anche in assenza di questa condizione di realizzabilità, cioè in assenza di una varietà Kähleriana associata. Nel seminario cercherò di dare un’idea di questo tipo di risultati e delle loro recenti estensioni.
2022
31 Marzo
Loredana Lanzani
Formule di rappresentazione integrale in più variabili complesse: il contributo fondamentale della scuola italiana

seminario interdisciplinare

Formule di rappresentazione integrale in più variabili complesse: il contributo fondamentale della scuola italiana Gli analoghi multidimensionali della celebre formula di Cauchy per le funzioni analitiche su un dominio nel piano costituiscono un capitolo relativamente recente nella lunga storia dell’analisi e della geometria complesse. Tali formule godettero di grande popolarità tra gli anni ’70 e gli anni ’90; recentemente stanno suscitando nuovo interesse grazie, in parte, alla scoperta di una feconda sinergia con la teoria di Calderón- Zygmund per gli operatori integrali singolari. In questo intervento rivisiteremo i risultati principali prestando particolare attenzione ai contributi fondamentali forniti da alcuni tra i leader storici dell'Unione Matematica Italiana. Integral Representation Formulas in Several Complex Variables: fundamental contributions of the Italian school Higher dimensional analogues of the celebrated Cauchy formula for analytic functions on a planar domain are a relatively recent chapter in the history of complex function theory and complex geometry. They were very popular in the 1970s through the 1990s and are experiencing renewed interest, thanks in part to a recently discovered, fruitful synergy with the Calderón-Zygmund theory of singular integral operators. In this talk we survey the main results and highlight fundamental contributions made by some of the historical leaders of the Italian Mathematical Union.
2022
31 Marzo
Umberto Bottazzini
1922-1942: I primi vent’anni di vita dell’UMI

seminario di storia della matematica

Nell'ambito della manifestazione UMI C UNIBO per il centenario dell'UMI. Abstract. A partire dalle discussioni che hanno accompagnato la ‘tardiva’ fondazione dell’Unione, il rapporto tra l’Unione e l’Università di Bologna fu inizialmente caratterizzato dall’attività svolta durante la presidenza di Salvatore Pincherle. Il primo ventennio di vita dell’UMI coincide col ventennio della dittatura fascista, e nella conferenza saranno messi in luce i numerosi intrecci che, a livello politico istituzionale, intercorsero tra la vita dell’Unione e il regime
2022
31 Marzo
Cristina Serra
La traduzione scientifica come possibile sbocco lavorativo per laureati in discipline scientifiche

seminario di didattica della matematica

Molte delle riviste scientifiche divulgative del panorama italiano (Le scienze, Mente e cervello, ...) pubblicano regolarmente traduzioni di articoli provenienti da riviste straniere. I traduttori di questo tipo di articoli devono possedere, oltre a competenze relative alle lingue, competenze scientifiche spesso non banali. Per questo molto difficilmente sono interpreti di professione, ma sono piuttosto persone di formazione scientifica, che si costruiscono un mestiere nel campo della traduzione. Nel seminario vedremo quali sono le qualifiche richieste, e tramite che strada si può iniziare una collaborazione di questo tipo.
2022
31 Marzo
Nicolas Perkowski
Introduction to singular SPDEs via paracontrolled distributions - Lecture III

seminario di analisi matematica, probabilità

3rd lecture: - regularity of the stochastic heat equation and its monomials - solution of the Phi-4-2 equation
2022
29 Marzo
Javier Aramayona (Instituto de Ciencias Matemáticas)
Asymptotic mapping class groups of Cantor manifolds and their finiteness properties
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

A Cantor manifold C is a non-compact manifold obtained by gluing (holed) copies of a fixed compact manifold Y in a tree-like manner. Generalizing braided Thompson groups, we introduce the asymptotic mapping class group of C, whose elements are proper isotopy classes of self-diffeomorphisms of C that are ”eventually trivial.” This group B happens to be an extension of a Higman-Thompson group by a direct limit of mapping class groups of compact submanifolds of C. B acts on a contractible cube complex X of infinite dimension. We use the action to determine finiteness properties of B: in well-behaved cases, X is CAT(0) and B is of type F∞. More concretely, the methods apply when Y is a 2-dimensional torus, S2 × S1, or Sn × Sn for n at least 3. In these cases, the group B contains the mapping class groups of every compact surface with boundary, the automorphism groups of every finitely generated free group, or an infinite familiy of arithmetic symplectic or orthogonal groups. In particular, the cases where Y is a sphere or a torus in dimension 2 yields a positive answer to a question of Funar-Kapoudjian-Sergiescu. In addition, we find cases where the homology of B coincides with the stable homology of the relevant mapping class groups. (Joint work with Kai-Uwe Bux, Jonas Flechsig, Nansen Petrosyan, and Xiaolei Wu.)
2022
29 Marzo
Nicolas
Introduction to singular SPDEs via paracontrolled distributions - Lecture II

seminario di analisi matematica, probabilità

2nd lecture: - paraproducts and Schauder estimates
2022
28 Marzo
Nicolas Perkowski
Introduction to singular SPDEs via paracontrolled distributions - Lecture I

seminario di analisi matematica, probabilità

1st lecture: - some examples of singular and non-singular SPDEs - distributions and function spaces
2022
25 Marzo
Ludovico Battista
Funzioni di Morse perfette a valori in S^1 su 4-varietà iperboliche
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

Lo studio delle varietà iperboliche e delle loro proprietà topologiche ha avuto un forte impatto nello studio delle varietà in dimensione bassa. La connessione tra la topologia di una varietà e il tipo di metrica che essa supporta ha portato al celebratissimo Teorema di Geometrizzazione in dimensione 3. In questa dimensione, le varietà iperboliche sono ampiamente le più complesse e le più studiate tra quelle che ammettono una geometria. In dimensione più alta la prominenza del ruolo delle varietà iperboliche è meno chiara. Non sembra però essere meno interessante chiedersi quali siano le proprietà topologiche che una 4-varietà iperbolica può avere. In questo seminario (e nel prossimo) daremo la definizione di funzione di Morse perfetta a valori in S^1 (in breve, PCVMF), e spiegheremo perché è interessante cercare varietà che ammettano una tale funzione. Richiameremo la costruzione di una varietà iperbolica mediante colorazione di politopi, e daremo un'idea di come sia possibile utilizzare questa struttura per costruire una PCVMF su una 4-varietà iperbolica.
2022
24 Marzo
Ermanno Lanconelli
Il ''problema di Dirichlet'' per l'equazione del calore: un metodo elementare

seminario di analisi matematica

Una delle maggiori difficoltà tecniche, nella risoluzione col metodo di Perron del ''Problema di Dirichlet'' per l'equazione del calore, è la costruzione di una base di aperti della topologia euclidea sui quali quel problema è risolubile. Nel seminario verrà dimostrato che la difficoltà si può superare in modo elementare, utilizzando un argomento tratto dalla teoria dei polinomi calorici, il principio del massimo e un semplice risultato di algebra lineare.
2022
23 Marzo
Nicola Lanaro e Marco Carlin (Cassa Centrale Banca)
Portafogli Modello per il Wealth Management

seminario di finanza matematica

2022
22 Marzo
Tommaso Rossi
Relative Heat Content Asymptotic for Sub-Riemmanian Manifolds

seminario di algebra e geometria

For a domain in M, the relative heat content is defined as the total amount of heat contained in the domain at time t, allowing the heat to flow outside the domain. We study the small-time asymptotics of the relative heat content associated with smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a technique due to Savo, we establish the existence of an asymptotic series, up to order 4. Significant difficulties emerges, as the boundary behavior of the temperature function is not known: we use an “asymptotic” symmetry argument of the heat diffusion to obtain information on the small-time behavior of temperature at the boundary of the domain. This is a joint work with Andrei Agrachev and Luca Rizzi.
2022
21 Marzo
Lorenzo Cerboni Baiardi
Characterization of synchronization patterns in nonlinear marketing models

seminario interdisciplinare

Some nonlinear discrete-time dynamic models of marketing competition are used to critically discuss the statement, often made in economic literature, according to which identical agents behave identically and quasi-identical ones behave accordingly. Under this assumption, the whole behavior of interacting agents is summarized by one-dimensional systems, describing the dynamics of so called representative agents. However, even in the simple two-dimensional case, the description in terms of a representative agent may be misleading. This occurs for example when riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors characterize the dynamic scenarios of the full system. To discuss the topic, some results from the theory of dynamical systems and chaos synchronization can be applied.
2022
18 Marzo
Leonardo Ferrari (Université de Neuchâtel)
Building manifolds from right-angled polytopes
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

Manifold covers of right-angled polytopes were first introduced by Davis and Januszkiewicz in 1991 as a simple, combinatorial method to build manifolds by gluing copies of a right- angled polytope along its facets. Since then a number of techniques have been added to their initial work, allowing for a better understanding of the geometry and topology of such manifolds, and many important, recent examples of hyperbolic 3-, 4- and 5-manifolds have arisen from this setting. In this seminar, I will introduce the notion of right-angled polytopes, present the basic construction of manifold covers and give an overview of some additional tools developed in recent years, as well as combinatorial and topological obstructions to the techniques. I will conclude the seminar with the construction of the first example of a hyperbolic, arithmetic, rational homology 3-sphere that bounds geometrically. Obs: no previous knowledge of hyperbolic or arithmetic geometry is required to follow this seminar, but some familiarity with base notions of algebraic topology is advised.
2022
18 Marzo
Andrea di Lorenzo
Integral Chow ring of moduli of stable 1-pointed curves of genus two

seminario di algebra e geometria

Moduli of curves play a prominent role in algebraic geometry. In particular, their rational Chow rings have been the subject of intensive research in the last forty years, since Mumford first investigated the subject. There is also a well defined notion of integral Chow ring for these objects: this is more refined, but also much harder to compute. In this talk I will present the computation of the integral Chow ring of moduli of stable 1-pointed curves of genus two, obtained by using a new approach to this type of questions (joint work with Michele Pernice and Angelo Vistoli).
2022
18 Marzo
Pierpaolo Vivo
LECTURE 6. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
17 Marzo
alessandra sarti
Complex reflection groups and K3 surfaces

seminario di algebra e geometria

2022
17 Marzo
Cyril Letrouit (ENS Paris)
Propagation of singularities in subelliptic PDEs

seminario di analisi matematica

In this talk, we consider the wave equation where the Laplacian is replaced by a sub-Laplacian (also called Hörmander sum of square''), which is an hypoelliptic operator. We handle the problem of describing the propagation of singularities in such equations : the main new phenomenon that we describe is that singularities can propagate along abnormal curves at any speed between 0 and 1. This general result extends an idea due to R. Melrose, and we then illustrate it on an example, the Martinet case, following a joint work with Y. Colin de Verdière. Our statements are part of a classical/quantum correspondance between sub-Riemannian geometry (on the classical side) and the hypoelliptic operator (on the quantum side), which is also helpful to interpret results in control theory and spectral theory of hypoelliptic operators.
2022
17 Marzo
emma Brakkee
Marked and labelled Gushel-Mukai fourfolds

seminario di algebra e geometria

2022
17 Marzo
Pierpaolo Vivo
LECTURE 5. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
16 Marzo
Jieao Song
Second Chern class and Fujiki constants of hyperkähler manifolds

seminario di algebra e geometria

2022
16 Marzo
Michal Kapustka
EPW sextics vs EPW cubes

seminario di algebra e geometria

2022
15 Marzo
Nicolò Forcillo
FREE BOUNDARY REGULARITY IN THE ONE-PHASE STEFAN PROBLEM. PART II

seminario di analisi matematica

In this seminar, a recent perturbative approach for the study of the free boundary regularity in the one-phase Stefan problem is presented. More precisely, we exhibit the fundamental steps of the method, whose main tool is an improvement of flatness property, in the spirit of the elliptic counterpart developed by D. De Silva. In this second part we will describe some technical results.
2022
15 Marzo
Annalisa Grossi
Symplectic birational transformations of finite order on O'Grady's sixfolds

seminario di algebra e geometria

2022
15 Marzo
Georg Oberdieck
Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface

seminario di algebra e geometria

2022
15 Marzo
Pierpaolo Vivo
LECTURE 4. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
14 Marzo
Ignacio Barros
On the birational geometry of the moduli of hyperelliptic curves

seminario di algebra e geometria

2022
14 Marzo
Pierpaolo Vivo
LECTURE 3. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
14 Marzo
Ekaterina Amerik
Parabolic automorphisms of hyperkahler manifolds

seminario di algebra e geometria

2022
14 Marzo
Lie Fu
Unpolarized Shafarevich conjectures for hyper-Kähler varieties

seminario di algebra e geometria

2022
11 Marzo
Stefano Riolo
Gruppi e politopi di Coxeter in geometria iperbolica (parte 2)
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

I gruppi di riflessione, il cui studio si può ricondurre alla Grecia antica con i poligoni e i poliedri, appaiono in svariate aree di ricerca della matematica contemporanea, tra cui algebra, analisi, combinatoria, dinamica, geometria, geometria algebrica, teoria dei numeri e topologia. Se ne parlerà da un punto di vista geometrico-topologico, con l'obiettivo utopistico di enunciare e dimostrare, magari più in là, qualcosa sulla topologia delle varietà iperboliche di dimensione non troppo alta.
2022
11 Marzo
Vincenzo Fano
La lunga storia dei paradossi dello spazio tempo
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
11 Marzo
Pierpaolo Vivo
LECTURE 2. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
10 Marzo
Claudia Lederman, University of Buenos Aires, Argentina
Free boundary regularity for a one-phase problem with non-standard growth

seminario di analisi matematica

We consider viscosity solutions to a one-phase free boundary problem for a nonlinear elliptic PDE with non-zero right hand side. We obtain regularity results for solutions and their free boundaries. The operator under consideration is a model case in the class of partial differential equations with non-standard growth. This type of operators have been used in the modelling of non-Newtonian fluids, such as electrorheological or thermorheological fluids, also in non-linear elasticity and image reconstruction. We also obtain some new results for the governing operator that are of independent interest. This is joint work with Fausto Ferrari (University of Bologna, Italy)
2022
10 Marzo
Pierpaolo Vivo
LECTURE 1. Random matrices: theory and practice
nel ciclo di seminari: RANDOM MATRICES: THEORY AND PRACTICE

seminario di fisica matematica, probabilità

2022
10 Marzo
Yannick Sire
Blow-up via parabolic gluing
We will present some recent results on the construction of blow-up solutions for critical parabolic problems of geometric flavor. Initiated in the recent years, the inner/outer parabolic gluing is a very versatile parabolic version of the well-known Lyapunov-Schmidt reduction in elliptic PDE theory. The method allows to prove rigorously some formal matching asymptotics (if any available) for several PDEs arising in porous media, geometric flows, etc….I will give an overview of the strategy and will present several applications to (variations of) the harmonic map flow, Yamabe flow and Yang-Mills flow. I will also present some open questions.
2022
08 Marzo
Jerzy Weyman (Jagiellonian University)
On the structure of Gorenstein ideals of codimension 4
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

I will discuss the new approach to Gorenstein ideals of codimension 4, with n generators. This allows us to construct (by a single calculation, starting from scratch) the examples of such ideals with 4<= n<= 8 generators. For n=4,5,6 they give generic models of resolutions of ideals of that type (in the sense that each such resolution comens from the generic model). We conjecture that for n=7,8 these resolutions are also generic models. The main idea is a construction of a certain generic ring which has unexpected symmetry of the type E_n. For n >= 9 such construction is not possible which indicates that the classification is much more difficult.
2022
07 Marzo
Rossella Agliardi
Optimal stopping problems arising in real option theory
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022

seminario di finanza matematica

I survey some results and open questions regarding the applications of optimal stopping theory to real option analysis. The main focus is on the issue of obtaining explicit solutions for the related free-boundary problems. First, some elementary examples are presented which are of interest for economic applications. Then an explicit expression for the value function in the two- dimensional (and n-dimensional ) case is obtained. The value function is written in terms of a modified Bessel function of second kind. Some useful formulas for the one-dimensional case are presented as well.
2022
04 Marzo
Stefano Riolo
Gruppi e politopi di Coxeter in geometria iperbolica
nell'ambito della serie: TOPOLOGIA E GEOMETRIA DELLE VARIETÀ

seminario di algebra e geometria

I gruppi di riflessione, il cui studio si può ricondurre alla Grecia antica con i poligoni e i poliedri, appaiono in svariate aree di ricerca della matematica contemporanea, tra cui algebra, analisi, combinatoria, dinamica, geometria, geometria algebrica, teoria dei numeri e topologia. Se ne parlerà da un punto di vista geometrico-topologico, con l'obiettivo utopistico di enunciare e dimostrare, magari più in là, qualcosa sulla topologia delle varietà iperboliche di dimensione non troppo alta.
2022
04 Marzo
Walter Cavini
I paradossi di Zenone nel contesto della storia della filosofia antica
nell'ambito della serie: SEMINARI PROGETTO VAST

seminario interdisciplinare

2022
04 Marzo
Michelangelo Cavina
A stochastic view of Caffarelli-Silvestre theorem
nell'ambito della serie: COMPLEX ANALYSIS LAB

seminario di analisi matematica, probabilità

Caffarelli and Silvestre gave a celebrated interpretation of the fractional Laplacian in terms of a Dirichlet problem for an elliptic operator. In this introductory and expository seminar we show how this can be viewed in terms of stochastic processes.
2022
01 Marzo
Nicolò Forcillo
Free boundary regularity in the one-phase Stefan problem. Part I

seminario di analisi matematica

In this seminar, a recent perturbative approach for the study of the free boundary regularity in the one-phase Stefan problem is presented. More precisely, we exhibit the fundamental steps of the method, whose main tool is an improvement of flatness property, in the spirit of the elliptic counterpart developed by D. De Silva.
2022
01 Marzo
Andreas Knutsen
Severi Varieties on Enriques Surfaces
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Given a (smooth) projective (complex) surface S and a complete linear (or algebraic) system of curves on S, one defines the Severi varieties to be the (possibly empty) subvarieties parametrizing nodal curves in the linear system, for any prescribed number of nodes. These were originally studied by Severi in the case of the projective plane. Afterwards, Severi varieties on other surfaces have been studied, mostly rational surfaces, K3 surfaces and abelian surfaces, often in connection with enumerative formulas computing their degrees. Interesting questions are nonemptiness, dimension, smoothness and irreducibility of Severi varieties. In this talk I will first give a general overview and then present recent results about Severi varieties on Enriques surfaces, obtained with Ciliberto, Dedieu and Galati, and the connection to a conjecture of Pandharipande and Schmitt.
2022
24 Febbraio
Antonio J. Fernandez
Desingularization of vortices for the generalized SQG equations

seminario di analisi matematica

We consider the generalized inviscid surface-quasigeostrophic equations (gSQG) and analyse the existence of a smooth compactly supported solution to the (gSQG) which is concentrated around N moving vortices. The result we discuss could be understood as the extension to the case of the (gSQG) of the seminal result of Marchioro and Pulvirenti concerning the bi-dimensional incompressible Euler equations. However, the information about the dynamic behaviour and the shape of the constructed solution that we obtain is much more precise than the obtained by Marchioro and Pulvirenti. The talk is based on a joint work with Manuel del Pino.
2022
24 Febbraio
Antonio J. Fernandez
Desingularization of vortices for the generalized SQG equations

seminario di analisi matematica

We consider the generalized inviscid surface-quasigeostrophic equations (gSQG) and analyse the existence of a smooth compactly supported solution to the (gSQG) which is concentrated around N moving vortices. The result we discuss could be understood as the extension to the case of the (gSQG) of the seminal result of Marchioro and Pulvirenti concerning the bi-dimensional incompressible Euler equations. However, the information about the dynamic behaviour and the shape of the constructed solution that we obtain is much more precise than the obtained by Marchioro and Pulvirenti. The talk is based on a joint work with Manuel del Pino.
2022
23 Febbraio
Alexander Bufetov
IL CAVALIERI OVVERO L’ENIGMA DEGLI INDIVISIBILI (a 375 anni dalla scomparsa)

seminario di storia della matematica

Bonaventura Cavalieri (1598 Milano – 1647 Bologna) è una figura sfingea nella storia della matematica. Pochissimo si sa della sua vita. Il suo magnum opus “Geometria indivisibilibus continuorum » rivoluzionò la teoria dell’integrale. In questa breve introduzione dedicata al grande pubblico cercheremo di recepire il contributo fondamentale del genio solitario e tenebroso.
2022
22 Febbraio
Marco Moraschini (Università di Bologna)
Simplicial volume and aspherical manifolds
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Simplicial volume is a homotopy invariant for compact manifolds introduced by Gromov in the early 80s. It measures the complexity of a manifold in terms of singular simplices. Since simplicial volume behaves similarly to the Euler characteristic, a natural problem is to understand the relation between these two invariants. More precisely, a celebrated question by Gromov (~’90) asks whether all oriented closed connected aspherical manifolds with zero simplicial volume also have vanishing Euler characteristic. In this talk, we will introduce the notion of simplicial volume and then we will describe Gromov's question. Then, we will discuss some new possible strategies to approach the problem as well as the relation between Gromov’s question and other classical problems in topology. This is part of a joint work with Clara Löh and George Raptis.
2022
17 Febbraio
Fabiana Leoni (Sapienza Università di Roma)
New concentration phenomena for radial solutions of fully nonlinear elliptic equations

seminario di analisi matematica

We present recent results about radial solutions of a class of fully nonlinear elliptic Dirichlet problems posed in a ball, driven by the extremal Pucci's operators and provided with power zero order terms. We show that a new critical exponent appears, related to the existence or nonexistence of sign-changing solutions. Furthermore we analyze the new concentration phenomena occurring as the exponents approach the critical values. Based on joint works with A. Iacopetti, G. Galise and F. Pacella.
2022
15 Febbraio
Giulio Tralli
Kolmogorov-type operators and Krylov-Safonov theory: state of the art and partial results

seminario di probabilità

In this talk we will discuss the validity of Harnack inequalities for linear evolution equations modelled after the Kolmogorov operator. The main focus will be on nondivergence form equations with non-smooth coefficients, and on the absence of an analogue of the ABP maximum principle and of the Krylov-Safonov theory in this setting. In particular, we will highlight as the (very general) crucial ingredient some quantitative point-to-measure estimate for nonnegative subsolutions. With this perspective in mind, we will show a potential theory approach (established in a 2019 joint work with F. Abedin) which allows to prove invariant Harnack inequalities for Kolmogorov-type operators with coefficients satisfying either a Cordes-Landis assumption or a continuity hypothesis.
2022
15 Febbraio
Stefano Riolo (Università di Bologna)
La segnatura delle 4-varietà iperboliche con cuspidi
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

Le 4-varietà iperboliche (orientate) compatte hanno segnatura nulla per il Teorema della segnatura di Hirzebruch. Cosa si può dire, invece, per 4-varietà non compatte, complete e di volume finito? In questo caso, la segnatura dipende solo dalla topologia delle parti finali (le cuspidi) e si annulla sempre su qualche rivestimento finito della varietà. Inoltre, tutti gli esempi noti fino a poco tempo fa avevano segnatura nulla. Considerazioni naïve potrebbero quindi dare la sensazione che questo sia vero in generale. Vedremo invece che la segnatura può essere qualsiasi numero intero e, tempo permettendo, affronteremo di conseguenza qualche considerazione "geografica". In collaborazione con Sasha Kolpakov e Steve Tschantz.
2022
15 Febbraio
Alessandro Della Corte (Università di Camerino)
Dynamics of interval maps with dense discontinuities

seminario di sistemi dinamici

Continuity is often taken as a defining assumption of topological dynamical systems. In the last years, however, increasing attention has been paid to the investigation of highly discontinuous maps from the point of view of topological dynamics. Continuity has been relaxed in ways allowing a dense set of discontinuous points: for instance Darboux, Baire 1 and 2, almost-continuous and quasi-continuous maps have been considered. There are good reasons, beyond the mere search for generality, for this research direction. The talk will discuss these reasons and will describe a particular class of densely discontinuous maps, i.e. those generated by the symbolic action of erasing substitutions on the binary expansion of reals in the unit interval.
2022
14 Febbraio
Dario Corona (Università di Camerino)
The critical exponent functions

seminario di sistemi dinamici

The critical exponent of a word is an important combinatorial concept which has applications in symbolic dynamics and transcendental number theory. It is natural to define a countable class of interval self-maps sending every real in [0,1] to the inverse of the critical exponent of its base-n expansion. In the investigation of these maps, an interesting interplay emerges between recent results on the dynamics of densely discontinuous maps and combinatorial properties of words. Moreover, these maps provide examples of semi-continuous maps with very rich dynamics. This can be a useful starting point for the systematic investigation of the topological dynamical properties of this kind of maps, which is yet to begin.
2022
10 Febbraio
Alessandro Oneto
On the strength of homogeneous polynomials
nel ciclo di seminari: GEOMETRIA ALGEBRICA E TENSORI

seminario di algebra e geometria

The strength of a homogeneous polynomial is the smallest length of an additive decomposition as sum of reducible forms. It is called slice rank if we additionally require that the reducible forms have a linear factor. Geometrically, the slice rank corresponds to the smallest codimension of a linear space contained in the hypersurface defined by the form. Due to this relation, it is well-known and easy to compute the value of the general slice rank and also to show that the set of forms with bounded slice rank is Zariski-closed. In this talk, I will present the following results from recent joint works with A. Bik, E. Ballico and E. Ventura: (1) the set of forms with bounded strength is not always Zariski-closed: this is an asymptotic result in the number of variables proved by using the theory of polynomial functors; (2) for general forms, strength and slice rank are equal: this is proved by showing that the largest component of the secant variety of the variety of reducible forms is the secant variety of the variety of forms with a linear factor.
2022
04 Febbraio
Isidoros Iakovidis
SZEMEREDI’S THEOREM IIi
nel ciclo di seminari: COMPLEX ANALYSIS LAB

seminario interdisciplinare

In this series of expository talks we introduce and discuss tools of ergodic theory such as recurrence theorems in order to give the proof of Szemeredi’s theorem.
2022
01 Febbraio
Giovanni Cerulli Irelli (Sapienza Università di Roma)
Symmetric representation theory of quivers and connections to Lie theory
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The representation theory of quivers and finite dimensional algebras deals with representations of products of general linear groups, and it is hence a type A situation''. There are many attempts to drag into the pictures groups of other nature. In this talk I will talk about a new attempt to get actions of groups of type B,C and D on the representation varieties associated to algebras with self-duality based on joint works with Magdalena Boos and partially with Francesco Esposito. For hereditary algebras this reduces to the approach due to Derksen and Weyman in 2002 when they introduced the so-called symmetric quivers''. In the first part I will mostly talk about quivers of type A and their symmetric representation theory, and state one of our main result with Lena which states that the symmetric orbit closures are induced by non-symmetric ones for symmetric quivers of finite type. Then I will talk about the connection with 2-nilpotent Borel orbits in classical Lie algebra worked out with Lena and Francesco and give an example that shows that in this context is not true the orbit closures of type D are induced by type A. I will close the talk by stating various conjectures and open problems concerning the problem of when symmetric orbit closures are induced by type A.
2022
01 Febbraio
Simonetta Abenda
KP soliton theory, dimer models in the disc and totally non-negative Grassmannians
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022

seminario di analisi matematica

Totally non-negative Grassmannians are a special case of G. Lusztig extension of the classical notion of total positivity, and have been combinatorially characterized in a seminal paper by A. Postnikov. They also appear in many relevant problems of mathematical and theoretical physics. The Kadomtsev-Petviashvili (KP) equation is the first non-trivial flow of the most relevant classical integrable hierarchy, and was originally introduced to study the stability of soliton solutions of another integrable system, the Kortweg-de Vries equation. Kasteleyn theorem represents the number of dimer configurations in planar graphs as determinants of sign matrices. In this talk I shall explain the role of totally non-negative Grassmannians in the characterization of the asymptotic behavior in space-time of a class of solutions of the Kadomtsev-Petviashvili equation, in the solution of a spectral problem for the same equation and in counting dimer configurations in planar bipartite graphs in the disc. The presentation will be elementary and self-contained.
2022
28 Gennaio
Isidoros Iakovidis
SZEMEREDI’S THEOREM II
nell'ambito della serie: COMPLEX ANALYSIS LAB

seminario interdisciplinare

In this series of expository talks we introduce and discuss tools of ergodic theory such as recurrence theorems in order to give the proof of Szemeredi’s theorem.
2022
27 Gennaio
Gregorio Chinni
On the regularity of solutions and of analytic vectors for `sums of squares"

seminario di analisi matematica

We present some results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of Hörmander type. Moreover we also illustrate a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hörmander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.
2022
21 Gennaio
Isidoros Iakovidis
Szemeredi’s theorem I
nell'ambito della serie: COMPLEX ANALYSIS LAB

seminario interdisciplinare

In this series of expository talks we introduce and discuss tools of ergodic theory such as recurrence theorems in order to give the proof of Szemeredi’s theorem.
2022
19 Gennaio
Marco Andreatta
Archimede, l'arte della misura

seminario interdisciplinare

Misurare lo spazio è cruciale per il nostro processo di conoscenza. Archimede è un pioniere della geometria, nella sua accezione più letterale di «misura della terra». Primo nel misurare enti curvi nello spazio e nel calcolare la superficie e il volume della sfera, fu geniale nel metodo, che affascinò tutti i grandi protagonisti della scienza moderna: da Galileo che ne riprenderà le dimostrazioni con una sensibilità nuova, a Gauss che ne estende i calcoli con conseguenze mirabolanti, fino a Einstein che con la sua Equazione di campo scopre una delle formule più famose della storia del pensiero scientifico, un’espressione che può essere pensata come la versione contemporanea della formula di Archimede.
2022
18 Gennaio
Marco Andreatta
Lifting from an ample section.The case of weighted blow-ups

seminario di algebra e geometria

A classical method to study a projective variety is to consider its hyperplane section and ”lift” the properties of the section to the variety. This is sometime called Aplollonius method and it works well since in general a variety is at least as special as any of its hyperplane sections. For example a weighted projective space can be an hyperplane section only of a weighted projective space (S. Mori 1975). We extend this result in a ”relative situation”, namely we consider f : X → Z to be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities and Y ⊂ X to be a f-ample Cartier divisor. If f|Y : Y → W has a structure of a weighted blow-up then f : X → Z, as well, has a structure of weighted blow-up. As an application we consider a local projective contraction f : X → Z from a variety X with terminal Q-factorial singularities, which contracts a prime divisor E to an isolated Q-factorial singularity P ∈ Z, such that −(KX + (n − 3)L) is f-ample, for a f-ample Cartier divisor L on X. Using the above result, the existence of a ”good” general section of L and the existing results in dimension 3, we prove that (Z,P) is a hyperquotient singularity and f is a weighted blow-up.
17/01/2022
18/01/2022
Samuele Mongodi, Politecnico di Milano, Italy
The Levi core of a pseudoconvex domain

seminario di algebra e geometria

2022
18 Gennaio
Alexander Bufetov
lezione 13
17/01/2022
18/01/2022
Bianca Gariboldi, Università degli studi di Bergamo, Italy
Cassels-Montgomery lemma and almost positive kernels on Riemannian manifolds

seminario di analisi matematica

17/01/2022
18/01/2022
Loredana Lanzani (UniBo)
The Cauchy–Szegö projection and its commutor for domains in C n with minimal smoothness: Optimal estimates

seminario di analisi matematica

17/01/2022
18/01/2022
Tommaso Bruno, Universiteit Gent, Belgium
Schrödinger operators on Lie groups with purely discrete spectrum

seminario di analisi matematica

17/01/2022
18/01/2022
Leandro Arosio, Università di Roma “Tor Vergata”, Italy
Horospheres in several complex variables

seminario di algebra e geometria

17/01/2022
18/01/2022
Alessandro Monguzzi Università di Bergamo, Italy
Euler-MacLaurin summation formulas on polyhedra

seminario di analisi matematica

17/01/2022
18/01/2022
Giulia Sarfatti, Università Politecnica delle Marche. Italy
An overview on the quaternionic Hardy space

seminario di analisi matematica

17/01/2022
18/01/2022
Federico Santagati, Politecnico di Torino, Italy
Riesz transform for a flow Laplacian on homogeneous trees

seminario di analisi matematica

17/01/2022
18/01/2022
Stefano Pinton, Politecnico di Milano, Italy
The subharmonicity index of higher order gradient of regular functions

seminario di algebra e geometria

17/01/2022
18/01/2022
Matteo Levi, Politecnico di Torino, Italy
BMO, Hardy spaces and Calderón-Zygmund theory on some nondoubling trees

seminario di analisi matematica

17/01/2022
18/01/2022
Alessio Martini, University of Birmingham, UK
Sharp multiplier theorems for Grushin operators

seminario di analisi matematica

17/01/2022
18/01/2022
Francesca Bartolucci, ETH Zürich, Switzerland
TBA

seminario di analisi matematica

17/01/2022
18/01/2022
Matteo Fiacchi, Università di Pisa, Italy
On the Gromov hyperbolicity of domains in C n

seminario di algebra e geometria

17/01/2022
18/01/2022
Matteo Monti, Università di Genova, Italy
Reproducing kernel for Bergman spaces on homogeneous trees

seminario di analisi matematica

17/01/2022
18/01/2022
Serena Federico, Universiteit Gent, Belgium
Strichartz estimates for some variable coefficient Schrödinger operators

seminario di analisi matematica

17/01/2022
18/01/2022
Carlo Bellavita, Università degli Studi di Milano La Statale, Italy
Boundedness of Translation operator in de Branges spaces

seminario di analisi matematica

17/01/2022
18/01/2022
Mattia Calzi, Università degli Studi di Milano La Statale, Italy
Carleson and Sampling Measures for Bergman Spaces on Homogeneous Siegel Domains

seminario di analisi matematica

17/01/2022
18/01/2022
Nikolaos Chalmoukis, Alma Mater Studiorum Universtità di Bologna, Italy