# Archivio 2019

14
Giu

2019
Francesca Colasuonno, Università di Torino
Some supercritical problems with Neumann boundary conditions

seminario di analisi matematica

14
Giu

2019
Eleonora Cinti
Some recent results in the study of fractional mean curvature flow

seminario di analisi matematica

14
Giu

2019
Andras Domokos
Recent results regarding the regularity of p-harmonic functions on Carnot groups

seminario di analisi matematica

14
Giu

2019
Enrico Valdinoci, University of Western Australia
Nonlocal minimal graphs in the plane are generically sticky

seminario di analisi matematica

14
Giu

2019
Italo Capuzzo Dolcetta
TBA (in the Workshop: Something about nonlinear problems)

seminario di analisi matematica

13
Giu

2019
Eugenio Vecchi, Università di Trento
TBA (in the Workshop: Something about nonlinear problems)

seminario di analisi matematica

13
Giu

2019
Fabrizio Anella
The twisted cotangent bundle of a hyperkahler manifold

seminario di algebra e geometria

Let X be a complex projective Hyperk ̈ahler manifold. By a recent result of H ̈oring and Peternell the cotangent bundle of X is not pseudoeffective. One way to measure this negativity more precisely is to give sufficient conditions on an ample line bundle A such that the twist ΩX ⊗ A is pseudoeffective. I will give a sufficient condition that depends only on the Segre classes and the Beauville–Fujiki form of X. Then I will discuss when this sufficent condition is also necessary. This is a joint work with Andreas H ̈oring.

13
Giu

2019
Some global Sobolev inequalities related to Kolmogorov-type operators

seminario di analisi matematica

13
Giu

2019
Serena Dipierro, University of Western Australia
A free boundary problem driven by the biharmonic operators

seminario di analisi matematica

13
Giu

2019
Giovanna Citti
TBA (in the Workshop: Something about nonlinear problems)

seminario di analisi matematica

13
Giu

2019
Juan Manfredi, Pittsburgh University
Random walks and random tug of war in the Heisenberg group

seminario di analisi matematica

11
Giu

2019
Mattia G. Bergomi, Pietro Vertechi
Persistenza topologica e non - 2

seminario di algebra e geometria

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other combinatorial, based on arbitrary set-valued functors. To unify the study of topological and combinatorial persistence in a common categorical framework, we give axioms for a generalized rank function on objects in a target category, so that functors to that category induce persistence functions. We port the interleaving and bottleneck distances to this novel framework and generalize classical equalities and inequalities. Unlike sets and vector spaces, in many categories the rank of an object does not identify it up to isomorphism: to preserve information about the structure of persistence modules, we define colorable ranks, persistence diagrams and prove the equality between multicolored bottleneck distance and interleaving distance in semisimple Abelian categories. To illustrate our framework in practice, we give examples of multicolored persistent homology on filtered topological spaces with a group action and labeled point cloud data. SLIDES - The ones of the present talk are here: https://mgbergomi.github.io/slideshow_bologna/ The ones of last week are attached.

10
Giu

2019
Gian Marco Todesco
Laboratorio PLS "Tecniche matematiche per l'animazione" - III incontro

nel ciclo di seminari: LABORATORIO PLS "TECNICHE MATEMATICHE PER L'ANIMAZIONE"

seminario interdisciplinare

07
Giu

2019
Gian Marco Todesco
Laboratorio PLS "Tecniche matematiche per l'animazione" - II incontro

nel ciclo di seminari: LABORATORIO PLS "TECNICHE MATEMATICHE PER L'ANIMAZIONE"

seminario interdisciplinare

07
Giu

2019
Maciej Zworski
Introduction to scattering resonances 4
Scattering resonances replace bound states/eigenvalues for spectral problems in which escape (scattering) to infinity is possible. These states have rates of oscillation and decay and that information is elegantly encoded in considering the corresponding eigenvalues" as poles of the meromorphic continuation of Green functions. The most famous pure maths" example is given by zeros of the Riemann zeta function which can be interpreted as resonances for scattering on the modular surface. In applied maths" they appear anywhere from gravitational waves to MEMS (Micro-Electro-Mechanical Systems). The mini course will provide a gentle introduction in the setting of potential scattering in dimension three. Only basic functional analysis will be a prerequisite. 1. One dimensional scattering: intuition behind outgoing and incoming waves and the definition of scattering resonances. 2. Analytic Fredholm theory and, as application, meromorphic continuation of Green's function for potentials scattering in dimension three. 3. Resonance free regions and expansion of waves in terms of resonances. 4. Counting resonances: upper bounds and existence (and some open problems). Complex valued potentials with no resonances. Section 2 of https://math.berkeley.edu/~zworski/revres.pdf (Bull Math Sci '17) will provide a reference with a more detailed presentation in the forthcoming book http://math.mit.edu/~dyatlov/res/ (AMS '19, to appear).

06
Giu

2019
Gian Marco Todesco
Laboratorio PLS "Tecniche matematiche per l'animazione" - I incontro

nel ciclo di seminari: LABORATORIO PLS "TECNICHE MATEMATICHE PER L'ANIMAZIONE"

seminario interdisciplinare

06
Giu

2019
Maciej Zworsi
Introduction to scattering resonances 3
Scattering resonances replace bound states/eigenvalues for spectral problems in which escape (scattering) to infinity is possible. These states have rates of oscillation and decay and that information is elegantly encoded in considering the corresponding eigenvalues" as poles of the meromorphic continuation of Green functions. The most famous pure maths" example is given by zeros of the Riemann zeta function which can be interpreted as resonances for scattering on the modular surface. In applied maths" they appear anywhere from gravitational waves to MEMS (Micro-Electro-Mechanical Systems). The mini course will provide a gentle introduction in the setting of potential scattering in dimension three. Only basic functional analysis will be a prerequisite. 1. One dimensional scattering: intuition behind outgoing and incoming waves and the definition of scattering resonances. 2. Analytic Fredholm theory and, as application, meromorphic continuation of Green's function for potentials scattering in dimension three. 3. Resonance free regions and expansion of waves in terms of resonances. 4. Counting resonances: upper bounds and existence (and some open problems). Complex valued potentials with no resonances. Section 2 of https://math.berkeley.edu/~zworski/revres.pdf (Bull Math Sci '17) will provide a reference with a more detailed presentation in the forthcoming book http://math.mit.edu/~dyatlov/res/ (AMS '19, to appear).

04
Giu

2019
Xavier Cabré, ICREA and Universitat Politècnica de Catalunya (Barcelona)
A gradient estimate for nonlocal minimal graphs

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

The talk will be concerned with s-minimal surfaces, that is, hypersurfaces of R^n with zero nonlocal mean curvature. These are the equations associated to critical points of the fractional s-perimeter. We will present a recent result in collaboration with M. Cozzi in which we establish, in any dimension, a gradient estimate for nonlocal minimal graphs. It leads to their smoothness, a result that was only known for n=2 and 3 (but without a quantitative bound); in higher dimensions only their continuity had been established. We will also present a work with E. Cinti and J. Serra in which we prove that half spaces are the only stable s-minimal cones in R^3 for s sufficiently close to 1.

04
Giu

2019
Alessandro Mella
Persistenza topologica e non - 1

seminario di algebra e geometria

Persistent Homology is one of the main tools of Topological Data Analysis. It consists in comparing, by homology, all pairs of sublevel sets of a pair (X, f) where X is a topological space (or a simplicial complex) and f is a real valued function on it. This produces a Persistence Diagram, a standard object which turns very useful in shape analysis and classification. But is the topological setup necessary for getting persistence diagrams? Massimo Ferri will introduce (classical) persistent homology in the first part. Alessandro Mella will then show a wide generalization of it and some initial applications.

04
Giu

2019
Maciej Zworski
Introduction to scattering resonances 2
Scattering resonances replace bound states/eigenvalues for spectral problems in which escape (scattering) to infinity is possible. These states have rates of oscillation and decay and that information is elegantly encoded in considering the corresponding eigenvalues" as poles of the meromorphic continuation of Green functions. The most famous pure maths" example is given by zeros of the Riemann zeta function which can be interpreted as resonances for scattering on the modular surface. In applied maths" they appear anywhere from gravitational waves to MEMS (Micro-Electro-Mechanical Systems). The mini course will provide a gentle introduction in the setting of potential scattering in dimension three. Only basic functional analysis will be a prerequisite. 1. One dimensional scattering: intuition behind outgoing and incoming waves and the definition of scattering resonances. 2. Analytic Fredholm theory and, as application, meromorphic continuation of Green's function for potentials scattering in dimension three. 3. Resonance free regions and expansion of waves in terms of resonances. 4. Counting resonances: upper bounds and existence (and some open problems). Complex valued potentials with no resonances. Section 2 of https://math.berkeley.edu/~zworski/revres.pdf (Bull Math Sci '17) will provide a reference with a more detailed presentation in the forthcoming book http://math.mit.edu/~dyatlov/res/ (AMS '19, to appear).

03
Giu

2019
Maciej Zworski
Introduction to scattering resonances 1
Scattering resonances replace bound states/eigenvalues for spectral problems in which escape (scattering) to infinity is possible. These states have rates of oscillation and decay and that information is elegantly encoded in considering the corresponding eigenvalues" as poles of the meromorphic continuation of Green functions. The most famous pure maths" example is given by zeros of the Riemann zeta function which can be interpreted as resonances for scattering on the modular surface. In applied maths" they appear anywhere from gravitational waves to MEMS (Micro-Electro-Mechanical Systems). The mini course will provide a gentle introduction in the setting of potential scattering in dimension three. Only basic functional analysis will be a prerequisite. 1. One dimensional scattering: intuition behind outgoing and incoming waves and the definition of scattering resonances. 2. Analytic Fredholm theory and, as application, meromorphic continuation of Green's function for potentials scattering in dimension three. 3. Resonance free regions and expansion of waves in terms of resonances. 4. Counting resonances: upper bounds and existence (and some open problems). Complex valued potentials with no resonances. Section 2 of https://math.berkeley.edu/~zworski/revres.pdf (Bull Math Sci '17) will provide a reference with a more detailed presentation in the forthcoming book http://math.mit.edu/~dyatlov/res/ (AMS '19, to appear).

31
Mag

2019
Xavier Cabré
Nonlocal minimal surfaces

nell'ambito della serie: COLLOQUIO DI DIPARTIMENTO

seminario interdisciplinare

In 2010 Caffarelli, Roquejoffre & Savin started the study of nonlocal minimal surfaces, that is, of hypersurfaces in Euclidean space with zero nonlocal mean curvature. This is the equation associated to critical points of the fractional perimeter. Among other motivations (such as image processing), they are relevant in phase-transition phenomena in the presence of long range interactions. Since their introduction, nonlocal minimal surfaces have attracted much attention, first and foremost to understand their regularity and to make progress towards their classification. We will describe the results obtained up to date, as well as the remaining open problems. As we will see, there is a remarkable resemblance with the classical theory of minimal surfaces.

31
Mag

2019
Dott. Amedeo Altavilla
TBA

seminario di analisi matematica

30
Mag

2019
Davide Guidetti
Un'applicazione del teorema di perturbazione di Miyadera a un problema misto iperbolico

seminario di analisi matematica

Consideriamo un problema misto lineare iperbolico del secondo ordine, con una condizione al contorno dinamica contenente anche un operatore ellittico sulla frontiera del dominio. Utilizzando un certo teorema di perturbazione per semigruppi fortemente continui (solitamente attribuito a Miyadera), estendiamo un caso particolare (essenzialmente gia' noto) a situazioni molto più' generali. Questi risultari sono applicabili anche al caso di condizioni al contorno di Wentzell.

30
Mag

2019
Brian Straughan
E-cigarette smoking with peer pressure - II

seminario di fisica matematica

A model is presented involving non-smokers, tobacco cigarette smokers, and those who smoke electronic cigarettes. The transfer from the tobacco smoker class to the e-cigarette class is via a peer pressure term. It is shown that there are three distinct equilibria. One involves no smokers of any kind. A second has only non-smokers and smokers of tobacco cigarettes. The third has a steady state with all three categories. Conditions are derived under which each equilibrium state will be stable. Numerical simulations are given that show the convergence to steady state for the third equilibrium. Simulations are also performed for a more general model where the peer pressure term in the tobacco to e-cigarette transition involves also a conformity bias.

29
Mag

2019
Giacomo Bormetti
An introduction to score-driven models

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

In recent years, dynamic conditional score-driven (DCS) models have attracted lot of interest in Economics, Finance, and Econometrics. However, their potential extends far beyond. The reason lies in the simplicity of the approach to time-series modelling and the easiness in parameter estimation. After presenting some motivating examples, in the first part of the talk I review the main theoretical properties of DCS models and discuss the flexibility of the approach in empirical applications. In the second part, I detail an application to high-frequency financial data. The approach has proved to be very effective in disentangling the fundamental price dynamics from micro-structure noise and in recovering the seasonal behaviour of prices at intra-day level.

28
Mag

2019
Amir Saki
The Lattice of Subracks of a Rack is Atomic and Complemented

seminario di algebra e geometria

A rack is a set R together with a binary operation ▷ such that • For each x, y, z ∈ R, x ▷ (y ▷ z) = (x ▷ y) ▷ (x ▷ z), and • for each x, y ∈ R, there exists a unique element z ∈ R with x ▷ z = y. If we have the extra condition x ▷ x = x for each x ∈ R, then R is called a quandle. For an example, a group G together with the operation x ▷ y = xyx−1 is a quandle. The study of racks and quandles dates back to 1943 when Takasaki used a certain algebraic structure to study reflections in finite geometries [?]. Since then, Racks and quandles have been used in some branches of mathematics such as knot theory for encoding knot diagrams. In 2015, I. Heckenberger et al. started the study of racks in a combined perspective of combinatorics and group theory. Indeed, they considered the lattice of subracks of a rack and obtained some interesting results [?]. Moreover, they posed some important questions in the last section of their paper. Two of these questions have been solved in [?] and [?]. Actually, it has been shown that the lattice of subracks of a rack is atomic, and this lattice for finite racks is complemented but there are some infinite racks whose lattices are not complemented.

28
Mag

2019
Brian Straughan
E-cigarette smoking with peer pressure - I

seminario di fisica matematica

A model is presented involving non-smokers, tobacco cigarette smokers, and those who smoke electronic cigarettes. The transfer from the tobacco smoker class to the e-cigarette class is via a peer pressure term. It is shown that there are three distinct equilibria. One involves no smokers of any kind. A second has only non-smokers and smokers of tobacco cigarettes. The third has a steady state with all three categories. Conditions are derived under which each equilibrium state will be stable. Numerical simulations are given that show the convergence to steady state for the third equilibrium. Simulations are also performed for a more general model where the peer pressure term in the tobacco to e-cigarette transition involves also a conformity bias.

28
Mag

2019
Alessandro Monguzzi
Spaces of Entire Functions in C^{n+1}

seminario di analisi matematica

A renowned space of entire functions of one complex variable is the Paley–Wiener space P W A , that is, the space of entire functions of exponential type A whose restriction to the real line is square integrable. In this talk I will present a generalization of P W A in several complex variables. In particular, I will consider entire functions which satisfy a suitable exponential growth condition and whose restriction to the boundary of the Siegel half-space satisfy some integrability conditions. For this space I will provide a Paley–Wiener type characterization and a sampling result. This is a joint work with Marco Peloso and Maura Salvatori.

28
Mag

2019
Bruno Benedetti
Grafi di politopi

seminario di algebra e geometria, interdisciplinare

I politopi (come cubi, piramidi, tetraedri...), studiati fin dagli albori della matematica, sono tuttora di moda anche grazie all'avvento della digitalizzazione e dell'ottimizzazione lineare. Il grafo di un politopo è semplicemente la struttura formata dai suoi vertici e dai suoi lati. Il diametro e la connettività di questi grafi sono di particolare interesse per le applicazioni. Parleremo di un approccio metrico (con K.Adiprasito) e di un approccio algebrico (con M. Varbaro, M. Dimarca, B.Bolognese) che stanno dando risultati promettenti.

24
Mag

2019
Ali Maalaoui
Prescribing the \bar{Q}'-Curvature on three dimensional Pseudo-Einstein Manifolds

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

24
Mag

2019
Stefano Biagi
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

24
Mag

2019
Farhan Abedin
Exponential convergence of Parabolic Optimal Transport on bounded domains

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

24
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 6

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

24
Mag

2019
Chiara Bianchini
A quantitative isoperimetric inequality in the plane

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

24
Mag

2019
Brian Straughan
Tridispersive thermal convection

seminario di fisica matematica

We derive the linear instability and nonlinear stability thresholds for a problem of thermal convection in a tridispersive porous medium with a single temperature. Importantly we demonstrate that the nonlinear stability threshold is the same as the linear instability one. The significance of this is that the linear theory is capturing completely the physics of the onset of thermal convection.

24
Mag

2019
Virginia Agostiniani
Minkowski inequality for mean convex domains

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

24
Mag

2019
Luciano Mari
On the 1/H flow via p-Laplace approximation under Ricci lower bounds

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Andrea Pinamonti
Γ-convergence for integral functionals depending on vector fields

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Chiara Guidi
Harnack inequality for a class of degenerate elliptic PDEs in non-divergence form

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Giulio Galise
Towards the critical exponents for fully nonlinear degenerate Lane-Emden type equations

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Annunziata Loiudice
Asymptotic decay results for critical growth equations

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Claudia Bucur
Symmetry in R^2 of global minimizers of a general type of nonlocal energy

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Berardo Ruffini
Sobolev immersions and Torsion functions

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

23
Mag

2019
Giulio Ciraolo
Symmetry results for critical p-Laplace equations

seminario di analisi matematica

Seminario nell'ambito della conferenza: Variational and PDE problems in Geometric Analysis, II

22
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 5

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

22
Mag

2019
Brian Straughan
Thermal convection in double porosity media

seminario di fisica matematica

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. The linear instability and nonlinear stability thresholds for a problem of thermal convection in bidispersive porous media with a single temperature are obtained and we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is able to capture completely the physics of the onset of thermal convection.

21
Mag

2019
Riccardo Biagioli
Elementi totalmente commutativi nei gruppi di Coxeter affini

seminario di algebra e geometria

Sia W un gruppo di Coxeter. Un elemento w di W è totalmente commutativo (TC) se prese due qualsiasi delle sue espressioni ridotte si può passare dall’una all’altra soltanto con una serie di scambi di generatori che commutano. Gli elementi TC sono stati studiati nel caso finito da Stembridge e indicizzano una base dell’algebra di Temperley-Lieb generalizzata associata a W. In questo talk daremo una classificazione degli elementi TC nel caso dei gruppi di Coxeter affini e mostreremo nel caso finito di tipo A e in quello affine di tipo \tilde{A} delle interpretazioni combinatorie che permettono il calcolo della funzione generatrice degli elementi TC secondo la lunghezza di Coxeter.

20
Mag

2019
Brian Straughan
Horizontally isotropic bidispersive thermal convection

seminario di fisica matematica

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. We present general equations for thermal convection in a bidispersive porous medium when the permeabilities, interaction coefficient and thermal conductivity are anisotropic but symmetric tensors. In this case, we show exchange of stabilities holds and fluid movement will commence via stationary convection, and additionally we show the global nonlinear stability threshold is the same as the linear instability one. Attention is then focused on the case where the interaction coefficient and thermal conductivity are isotropic, and the permeability is isotropic in the horizontal directions, although the permeability in the vertical direction is different. The nonlinear stability threshold is calculated in this case and numerical results are presented and discussed in detail.

20
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 4

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

20
Mag

2019
A. Zampini
Derivations base differential calculi on a class of Lie type non commutative spaces.

seminario di algebra e geometria

In this talk we shall present how the embedding of 3 dimensional Lie algebras g within the 4 dimensional Moyal space allows to define a differential calculus on non commutative spaces deforming the foliation coming from the coadjoint action of g on its dual. This differential calculus has a frame, so the spaces turn to be parallelisable.

20
Mag

2019
Stefan Kolb
Symmetric pairs for Nichols algebras of diagonal type

seminario di algebra e geometria

The theory of quantum symmetric pairs provides coideal subalgebras of quantum groups which give rise to braided module categories over braided monoidal categories. In this talk I will outline a program to extend the theory of quantum symmetric pairs to a setting of (pre-)Nichols algebras (of diagonal type). I will explain how the resulting coideal subalgebras are obtained via star products on partial bosonizations. This new perspective allows a conceptual, bar-involution free interpretation of the quasi K-matrix, which is the crucial ingredient in the construction of the braiding on the corresponding module category. The talk is based on joint work with Milen Yakimov.

17
Mag

2019
Marco Francischello
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

17
Mag

2019
Andrea Pallavicini
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

17
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 3

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

17
Mag

2019
Marco Francischello
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

17
Mag

2019
Andrea Pallavicini
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

16
Mag

2019
Annalisa Baldi
Poincaré and Sobolev inequalities for differential forms on Euclidean spaces and Heisenberg groups.

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

In this talk we present some recent results obtained in collaboration with B. Franchi and P. Pansu about Poincaré and Sobolev inequalities in Heisenberg groups (some results are new also for Euclidean spaces). For $L^p$, $p>1$, the estimates are consequence of singular integral estimates. I would like to concentrate the seminar, in particular, to the limiting case $L^1$, where the exterior Rumin-differential of a differential form is measured in $L^1$ norm. Unlike for $L^p$, $p>1$, the estimates are doomed to fail in top degree. In the limiting case, the singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis and Lanzani-Stein in Euclidean spaces, and to Chanillo-Van Schaftingen and Baldi-Franchi-Pansu in Heisenberg groups.

16
Mag

2019
Marco Francischello
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

16
Mag

2019
Luca Calatroni
“Mathematical imaging models for digital art conservation and restoration”

seminario di analisi numerica

16
Mag

2019
Andrea Sacchetti
Nonlinear Schroedinger equations: theory and applications

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

In this talk we discuss some recent results for a class of nonlinear models in Quantum Mechanics. In particular, in the first lecture we review some general results concerning the nonlinear Schroedinger equation; while in the second lecture we discuss in detail an explicit model: the one-dimensional nonlinear Schroedinger equation with a symmetric double-well potential.

16
Mag

2019
Andrea Pallavicini
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

16
Mag

2019
Marco Francischello
Spring School 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

16
Mag

2019
Andrea Pallavicini
Spring School in Finance 2019 on XVA modeling

nel ciclo di seminari: SEMINARI DI FINANZA MATEMATICA

seminario di probabilità

15
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 2

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

14
Mag

2019
Luca Marchese
Approssimazioni diofantee, dimensione e formalismo termodinamico per gruppi Fuchsiani

seminario interdisciplinare

Nella teoria classica delle approssimazioni diofantee l'insieme "Bad" è costituito dai numeri reali che sono male approssimabili dai razionali: si tratta di un insieme di misura zero e dimensione uno nella retta reale. Proprietà metriche più fini sono state studiate in dettaglio, sia nel caso classico che in varie generalizzazioni, in contesti legati alla dinamica su spazi omogenei ed altri spazi di moduli. L'insieme Bad ammette un'esaustione in sottoinsiemi Bad(c), la cui dimensione converge a 1 quando il parametro c>0 tende a zero. Nel caso classico D. Hensley ha ottenuto il primo ordine in c nello sviluppo asintotico della dimensione, attraverso un'analoga stima della dimensione dell'insieme dei numeri reali la cui frazione continua ha tutti i coefficienti parziali uniformemente limitati. Presenterò una generalizzazione della formula asintotica di Hensley nel contesto dei gruppi Fuchsiani, considerando l'insieme dei punti del bordo dello spazio iperbolico che sono male approssimabili per l'azione di un lattice non-uniforme G in PSL(2,R) ed un'esaustione di tale insieme in sottoinsiemi Bad(G,c), in termini di un parametro c>0. L'"espansione al bordo" di Bowen e Series permette di approssimare Bad(G,c) con insiemi di Cantor definiti dinamicamente, la cui dimensione può essere stimata con grande precisione tramite tecniche di formalismo termodinamico introdotte da Ruelle e Bowen. Un'analisi perturbativa del raggio spettrale dell'operatore di trasferimento fornisce la dimensione di Bad(G,c) al primo ordine in c.

13
Mag

2019
Gerardo Mendoza
Topics in Global Analysis - 1

nel ciclo di seminari: TOPICS IN GLOBAL ANALYSIS.

seminario interdisciplinare

13
Mag

2019
Tiziano De Angelis (The University of Leeds)
Probabilistic results concerning smoothness of the value function and of the free boundary in optimal stopping

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

I will present probabilistic proofs of some regularity properties for the value function of general optimal stopping problems and for the associated optimal boundaries. In particular this talk focusses on C^1 regularity of the value function and Lipschitz continuity of the optimal boundary. Most of our arguments rely on fundamental concepts from the theory of Markov processes and bridge the probabilistic and the analytical strands of the literature on free boundary problems. I will also illustrate situations in which our work improves or complements known facts from PDE theory.

10
Mag

2019
Luca Giudici
Dalle coordinate alla equivalenza: la conquista di von Neumann: II parte
Da uno spazio vettoriale V si ricava il sistema dei sottospazi lineari L, ordinato per inclusione, e l'anello degli endomorfismi R. Escludendo dim(V)<3, e con cura se dim(V)=3, seguendo von Staudt da L si ricostruisce V, e seguendo Birkhoff / Menger si caratterizza L, ma NON si ha una equivalenza. Generalizzando a moduli (o oggetti abeliani) V tali che ogni endomorfismo ha nucleo e immagine sommandi diretti, seguendo von Neumann si ha una equivalenza tra R e L, che si caratterizzano come anelli con inversa generalizzata (ogni x ha un y tale che xyx=x) e reticoli modulari complementati, con un sistema di unità matriciali di ordine n>2 in R e una base omogenea di ordine n in L (arguesiano se n=3). Il contesto generale chiarisce che V si ricostruisce solo a meno di equivalenze di Morita. L'equivalenza di von Neumann è archetipica per studiare altri casi. Due sono notevoli: [1] Partendo da uno spazio di Hilbert H, si ha una equivalenza tra gli anelli con involuzione A di operatori lineari continui tali che A=A'' (dove X' indica l'anello degli operatori che commutano con ogni x in X) e gli associati poset con involuzione P(A) delle proiezioni (idempotenti autoaggiunti, ordinati per divisibilità ef=e, con 1-e ortocomplemento di e), sempre escludendo i casi in cui una immagine omomorfa sia del tipo escluso sopra per V. Per i fondamenti logici della meccanica quantistica (i casi esclusi hanno intepretazione logico - quantistica della loro esclusione), von Neumann era particolarmente interessato al sottocaso indecomponibile (e=0,1 le uniche proiezioni che danno una decomposizione diretta) e finito'' (xy=1 implica yx=1 in A, ovvero P(A) modulare): von Neumann caratterizza P(A) come geometria continua con ortogonalità che permette libera mobilità e univocamente determina una probabilità di transizione; A è l'anello degli elementi limitati (sottoanello generato dalle proiezioni) dentro l'anello R associato a L=P(A). [2] Altri tipi di moduli (o oggetti abeliani) V ammettono una equivalenza come sopra, per esempio il caso di Baer - Inaba - J\'onsson / Monk dei moduli su anelli artiniani a ideali principali, caso che include i gruppi abeliani finiti e gli spazi vettoriali finito dimensionali con l'azione di una trasformazione lineare o antilineare. Se l'equivalenza per un singolo V è rara, accade invece sempre che una catagoria abeliana di vari V si ricostruisca dal reticolo associato. Il risutato finale (combinando Freyd - Mitchell per categorie abeliane e il teorema di G. Hutchinson per i reticoli) è che tre teorie in tre diversi linguaggi permettono di fare le stesse cose: (algebra lineare classica) moduli su un anello (algebra lineare moderna) categorie abeliane (geometria d'incidenza sintetica moderna) reticoli modulari con 0 in cui gli elementi sono raddoppiabili: $\forall x\exists y,z$: $x\vee y=y\vee z=z\vee x$ & $x\wedge y=y\wedge z=z\wedge x=0.$

09
Mag

2019
Ermanno Lanconelli
Mean value formulas and Liouville theorems for linear second order PDEs

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

We present several Mean Value formulas for solutions to linear second order PDEs endowed with smooth ''local fundamental solutions''. We then show how these formulas can be used to obtain Liouville Theorems for entire solutions. Our formulas are, in general, weighted average formulas. The relevant weights are ''densities with the mean value property'' a notion playing a central role in rigidity and stability problems. The results we present, related to the Mean value formulas, are obtained in collaboration with Giovanni Cupini. The ones related to the Liouville Theorems are joint works with Alessia Kogoj.

09
Mag

2019
Luca Calatroni
Metodi variazionali e PDE per l’elaborazione delle immagini

seminario di analisi numerica

Corso di Dottorato "Metodi variazionali e PDE per l’elaborazione delle immagini"- Cicli di seminari In this course we will present some classical and recent approaches for some problems in image reconstruction (denoising, deblurring, inpainting, shadow-removal…) formulated in terms of appropriate minimisation problems in infinite-dimensional functional spaces. We will further draw connections between these minimisation problems and parabolic Partial Differential Equations (PDEs) based on non-linear diffusion and possibly combined with transport terms. For the practical implementation of the models above, we will review standard finite difference stencils discussing their extensions to anisotropic diffusion and diffusion-transport problems. The course will be complemented by some practical MATLAB classes where simple exemplar problems will be solved by means of some reference iterative algorithms. Classical examples of imaging problems (denoising, deblurring, inpainting, segmentation..). Formulation as ill-posed inverse problems. Variational regularisation methods: regularisation term VS data fitting. Statistical interpretation: MAP estimation (2h) Sobolev spaces, standard methods in calculus of variations: a review. Total variation, the space of functions of bounded variations (2h) Second-order parabolic PDEs for image processing: heat equation, mean-curvature flow. Applications to image processing: linear VS non-linear PDEs. Regularisation of non-smoothness: lagged diffusivity. Anisotropic diffusion and diffusion-transport problems. (4h) Finite differences stencils for PDE-based imaging models. (2h) Numerical implementation and simulations in MATLAB for PDE-based models for image reconstruction (deblurring, inpainting, face fusion). (5h) Gli orari e le aule saranno specificati alla pagina web del dottorato ed inviati di volta in volta secondo il calendario 9/5: 2h (Teoria), mattina - 10/5: 2h (Teoria), mattina - 13/5: 2h (Teoria), mattina 14/5: 2h (Laboratorio), mattina 15/5: 2h (Teoria), mattina + 1h (Laboratorio), pomeriggio 16:5: 2h (Teoria), mattina - 17/5: 2h (Laboratorio), mattina

08
Mag

2019
Margherita Porcelli
Interior Point Methods for Linear, Quadratic and Nonlinear Programming

nel ciclo di seminari: MARGHERITA PORCELLI

seminario di analisi numerica

07
Mag

2019
ALBERTO SARACCO
Matematica e fumetti

seminario interdisciplinare

La scienza in generale (e la matematica in particolare) sono sempre state presenti nei fumetti Disney. Nei 70 anni di storia di Topolino libretto sono apparse quasi ventimila storie sul principale fumetto Disney italiano, e ci sono quindi centinaia di storie in cui appare la matematica. In questo seminario analizzeremo i vari diversi usi della matematica all'interno delle storie di topi e paperi. Passeremo poi a descrivere la recente collana di storie scientifiche Topolino Comic&Science, a cui per la matematica hanno collaborato Roberto Natalini del CNR di Roma e il sottoscritto. Infine analizzeremo un possibile utilizzo laboratoriale nelle scuole del fumetto "Paperino e i ponti di Quackenberg" per l'apprendimento di alcuni rudimenti di teoria dei grafi, combinatoria e del concetto di dimostrazione.

07
Mag

2019
Daniele Celoria
Cobordismi razionali e omologia intera II

seminario di algebra e geometria

Nella prima parte introdurremo alcune nozioni basilari della "topologia in dimensione 3.5", e in particolare il gruppo di concordanza per nodi, i gruppi di cobordismo intero e razionale, e le loro relazioni. Richiameremo quindi la classificazione degli spazi lenticolari a meno di cobordismo razionale. Nella seconda parte enunceremo alcuni nostri risultati; in particolare dimostreremo che all'interno del sottogruppo dei lenticolari e' sempre possibile trovare rappresentanti la cui omologia a coefficienti interi si inietta nell'omologia di ogni altro elemento nella classe. Discuteremo infine alcune conseguenze. Tra queste, alcuni risultati di struttura per il gruppo di cobordismo razionale, criteri di divisibilita' per concordanze per nodi a 2 ponti e stime per il problema di Berge razionale ottenute applicando l'omologia di Heegaard Floer per nodi.

07
Mag

2019
Margherita Porcelli
Interior Point Methods for Linear, Quadratic and Nonlinear Programming

nel ciclo di seminari: MARGHERITA PORCELLI

seminario di analisi numerica

07
Mag

2019
Paolo Aceto
Cobordismi razionali e omologia intera Parte I

seminario di algebra e geometria

Nella prima parte introdurremo alcune nozioni basilari della "topologia in dimensione 3.5", e in particolare il gruppo di concordanza per nodi, i gruppi di cobordismo intero e razionale, e le loro relazioni. Richiameremo quindi la classificazione degli spazi lenticolari a meno di cobordismo razionale. Nella seconda parte enunceremo alcuni risultati; in particolare dimostreremo che all'interno del sottogruppo dei lenticolari e' sempre possibile trovare rappresentanti la cui omologia a coefficienti interi si inietta nell'omologia di ogni altro elemento nella classe. Discuteremo infine alcune conseguenze. Tra queste, alcuni risultati di struttura per il gruppo di cobordismo razionale, criteri di divisibilita' per concordanze per nodi a 2 ponti e stime per il problema di Berge razionale ottenute applicando l'omologia di Heegaard Floer per nodi.

06
Mag

2019
Luca Giudici
Dalle coordinate alla equivalenza: la conquista di von Neumann: I parte

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

Da uno spazio vettoriale V si ricava il sistema dei sottospazi lineari L, ordinato per inclusione, e l'anello degli endomorfismi R. Escludendo dim(V)<3, e con cura se dim(V)=3, seguendo von Staudt da L si ricostruisce V, e seguendo Birkhoff / Menger si caratterizza L, ma NON si ha una equivalenza. Generalizzando a moduli (o oggetti abeliani) V tali che ogni endomorfismo ha nucleo e immagine sommandi diretti, seguendo von Neumann si ha una equivalenza tra R e L, che si caratterizzano come anelli con inversa generalizzata (ogni x ha un y tale che xyx=x) e reticoli modulari complementati, con un sistema di unità matriciali di ordine n>2 in R e una base omogenea di ordine n in L (arguesiano se n=3). Il contesto generale chiarisce che V si ricostruisce solo a meno di equivalenze di Morita. L'equivalenza di von Neumann è archetipica per studiare altri casi. Due sono notevoli: [1] Partendo da uno spazio di Hilbert H, si ha una equivalenza tra gli anelli con involuzione A di operatori lineari continui tali che A=A'' (dove X' indica l'anello degli operatori che commutano con ogni x in X) e gli associati poset con involuzione P(A) delle proiezioni (idempotenti autoaggiunti, ordinati per divisibilità ef=e, con 1-e ortocomplemento di e), sempre escludendo i casi in cui una immagine omomorfa sia del tipo escluso sopra per V. Per i fondamenti logici della meccanica quantistica (i casi esclusi hanno intepretazione logico - quantistica della loro esclusione), von Neumann era particolarmente interessato al sottocaso indecomponibile (e=0,1 le uniche proiezioni che danno una decomposizione diretta) e finito'' (xy=1 implica yx=1 in A, ovvero P(A) modulare): von Neumann caratterizza P(A) come geometria continua con ortogonalità che permette libera mobilità e univocamente determina una probabilità di transizione; A è l'anello degli elementi limitati (sottoanello generato dalle proiezioni) dentro l'anello R associato a L=P(A). [2] Altri tipi di moduli (o oggetti abeliani) V ammettono una equivalenza come sopra, per esempio il caso di Baer - Inaba - J\'onsson / Monk dei moduli su anelli artiniani a ideali principali, caso che include i gruppi abeliani finiti e gli spazi vettoriali finito dimensionali con l'azione di una trasformazione lineare o antilineare. Se l'equivalenza per un singolo V è rara, accade invece sempre che una catagoria abeliana di vari V si ricostruisca dal reticolo associato. Il risutato finale (combinando Freyd - Mitchell per categorie abeliane e il teorema di G. Hutchinson per i reticoli) è che tre teorie in tre diversi linguaggi permettono di fare le stesse cose: (algebra lineare classica) moduli su un anello (algebra lineare moderna) categorie abeliane (geometria d'incidenza sintetica moderna) reticoli modulari con 0 in cui gli elementi sono raddoppiabili: $\forall x\exists y,z$: $x\vee y=y\vee z=z\vee x$ & $x\wedge y=y\wedge z=z\wedge x=0.$

02
Mag

2019
Salvatore Cuomo
Metodi di collocazione RBF con applicazioni

seminario di analisi numerica

The Radial Basis Function (RBF) numerical methods are widely adopted methodologies for solving Partial Differential Equations (PDEs) via collocation schemes. These approaches do not require data structures and are generally known as meshfree methods. In this research field, an important issue to be addressed is related to the accuracy of the computed solution that may suffers from instability due to the ill-conditioning of the interpolation matrices. In this talk, the RBF collocation methods will be discussed for three case studies: i) the source-type ows in porous media problems; ii) a financial application to option pricing; iii) the implicit surface reconstruction.

02
Mag

2019
Lucia Romani
Subdivision schemes and numerical linear algebra

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

This talk is devoted to the topic of subdivision schemes, a special class of iterative methods for generating continuous curves and surfaces via the recursive application of suitable local refinement rules to a coarse initial set of prescribed control points. Due to their efficiency and simplicity of implementation, subdivision schemes are ones of the most used representation models in computer graphics and animation. Recently, they have shown their usefulness also in different areas of application like biomedical imaging and isogeometric analysis. Important tools for both the construction of linear subdivision schemes and the analysis of their properties are provided by classical numerical linear algebra techniques or adequate modifications of them. In particular, the construction of interpolatory subdivision schemes capable of generating curves and surfaces that pass through the initial set of prescribed control points, relies on algebraic strategies that differ according to the symmetry properties of the underlying refinement rules. The goal of this talk is to show some of the constructive strategies proposed in the literature for the subclass of stationary, odd- and even-symmetric, interpolatory subdivision schemes of arbitrary arity.

02
Mag

2019
Salvatore Cuomo
Collocation Methods based on Radial Basis Functions with Applications

seminario di analisi numerica

The Radial Basis Function (RBF) numerical methods are widely adopted methodologies for solving Partial Differential Equations (PDEs) via collocation schemes. These approaches do not require data structures and are generally known as meshfree methods. In this research field, an important issue to be addressed is related to the accuracy of the computed solution that may suffers from instability due to the ill-conditioning of the interpolation matrices. In this talk, the RBF collocation methods will be discussed for three case studies: i) the source-type flows in porous media problems; ii) a financial application to option pricing; iii) the implicit surface reconstruction.

30
Apr

2019
Andrea Brini
Elementi centrali in U(gl(n)) , funzioni Shifted Simmetriche, Basi di Sahi/Okounkov/Schur, immananti quantici e immananti di Capelli (parte seconda)

seminario di algebra e geometria

ll centro ζ(n) dell’inviluppo universale U(gl(n)) è isomorfo all’algebra ∧∗(n) dei polinomi shifted-simmetrici, via l’isomorfismo di Harish Chandra. L’algebra ∧∗(n)ammette una base (lineare) molto rilevante, costituita dai polinomi di Schur shifted-simmetrici, scoperti e caratterizzati da Kostant e Sahi, poi studiati sistematicamente da Okounkov, Olshanski et al. ll problema di descrivere/studiare gli elementi centrali in U(gl(n)) che corrispondono ai polinomi di Schur shifted-simmetrici è stato studiato da Okounkov in una serie lavori, tramite la nozione di immanante quantico. Gli immananti quantici sono elementi di ζ(n) assai difficilmente trattabili, come commentato dallo stesso Okounkov. Si è sviluppata una teoria sistematica degli immananti quantici e del centro ζ(n) basata sulla nuova nozione di immanante di Capelli in U(gl(n)). Gli immananti di Capelli sono una generalizzazione sia degli immananti classici (Littlewood/Richardson, 1934) di una matrice ad entries commutativi, sia del celebre determinante di Capelli in U(gl(n)), sono efficacemente trattabili, e formano un sistema di generatori lineari (compatibili con la filtrazione naturale di U(gl(n)). Gli immananti quantici di Okounkov risultano semplici combinazioni lineari di immananti di Capelli. ll passaggio al limite n→ ∞ per ζ(n) e ∧∗(n) si descrive esplicitamente come limite diretto rispetto alla decomposizione/proiezione Olshanski.

30
Apr

2019
Margherita Porcelli
Interior Point Methods for Linear, Quadratic and Nonlinear Programming

nel ciclo di seminari: MARGHERITA PORCELLI

seminario di analisi numerica

18
Apr

2019
Francesco Guerra
Symmetrization method in statistical mechanics

seminario di fisica matematica

In this talk we discuss the so called symmetrization method and its applications to statistical mechanics.

17
Apr

2019
Luigi Ambrosio
Calculus, heat flow, optimal transport and curvature-dimension bounds in metric measure spaces

nell'ambito della serie: COLLOQUIO DI DIPARTIMENTO

In this survey lecture, modelled in large part on the ICM2018 one, I will illustrate the most recent developments on calculus in metric measure spaces and the key role played by the theory of optimal transport in the derivation of synthetic lower bounds on Ricci curvature and upper bounds on dimension, for metric measure structures. If time permits, I will also illustrate the emerging role of optimal transport and gradient flows in the field of machine learning.

15
Apr

2019
Elena Magnanini
Un’indagine numerica sulla funzione dei cumulanti dell’osservabile triangoli nel modello denso di Erdӧs-Rényi

seminario di probabilità

Il calcolo della probabilità degli eventi rari è l’obiettivo principale della teoria delle grandi deviazioni. Per esempio, in un caso semplice, si può considerare l’evento in cui una somma di variabili aleatorie di Bernoulli raggiunge un valore che è più grande della sua media. Un problema completamente differente e più complesso, è il calcolo delle grandi deviazioni di funzionali non lineari di variabili Bernoulliane, come per esempio i polinomi cubici. Un ambito in cui un problema di questo tipo insorge è, per esempio, lo studio delle reti complesse. In questo seminario presenterò il comportamento della funzione dei cumulanti (scaled cumulant generating function) del numero dei triangoli nel contesto del modello denso di Erdӧs-Rényi. La funzione dei cumulanti è strettamente connessa alla teoria delle grandi deviazioni in quanto, quando è possibile applicare il teorema di Gärtner-Ellis, essa risulta essere la trasformata di Legendre della funzione delle grandi deviazioni. L’obiettivo di questa comunicazione è duplice: da un lato, descrivere l’estensione di un noto metodo Monte Carlo, chiamato algoritmo Cloning, formalizzata per approssimare la funzione dei cumulanti di un’osservabile additiva nel contesto dei grafi random. Dall’altro, mantenendo il focus sull’osservabile triangoli, presentare l’indagine numerica che è stata svolta nella regione dei parametri dove l’espressione analitica di tale funzione non è nota (regime di rottura delle repliche).

11
Apr

2019
Menita Carozza
On weakly monotone functions
The notion of weakly monotone functions was introduced, in the setting of Sobolev spaces, by J.Manfredi, in connection with the analysis of the regularity of maps of finite distortion appearing in the theory of nonlinear elasticity. We propose a criterion for the continuity of weakly monotone functions in terms of the decreasing rearrangement of their gradient. We also prove the continuity of weakly monotone functions whose gradient is in suitable rearrangement-invariant spaces. In particular, weakly monotone functions with gradient belonging to an Orlicz space or to a Lorentz space are discussed. These results are contained in joint works with Andrea Cianchi.

09
Apr

2019
Federico Camia
Limit Laws and Conformal Ensembles in the Planar Ising Model

seminario di fisica matematica

In the last twenty years there has been tremendous progress in the mathematical understanding of phase transitions for models of statistical mechanics defined on planar lattices. Much of that progress is related to the study of scaling limits, obtained by sending the lattice spacing to zero. In this talk I will give a brief introduction to scaling limits and present some recent results in the mathematical theory of phase transitions. I will focus on the case of the Ising model, which was introduced in the 1920s to study ferromagnetism and is one of the most studied models of statistical mechanics. I will discuss the convergence of the Ising magnetization to a random field (i.e., a random generalized function) with interesting properties of conformal covariance, and the connection with Euclidean field theory and the associated quantum field theory. (Based on collaborations with Rene Conijn, Christophe Garban, Jianping Jiang, Demeter Kiss, and Chuck Newman.)

09
Apr

2019
Andrea Brini
Elementi centrali in U(gl(n)) , funzioni Shifted Simmetriche, Basi di Sahi/Okounkov/Schur, immananti quantici e immananti di Capelli (parte prima)

seminario di algebra e geometria

ll centro ζ(n) dell’inviluppo universale U(gl(n)) è isomorfo all’algebra ∧∗(n) dei polinomi shifted-simmetrici, via l’isomorfismo di Harish Chandra. L’algebra ∧∗(n)ammette una base (lineare) molto rilevante, costituita dai polinomi di Schur shifted-simmetrici, scoperti e caratterizzati da Kostant e Sahi, poi studiati sistematicamente da Okounkov, Olshanski et al. ll problema di descrivere/studiare gli elementi centrali in U(gl(n)) che corrispondono ai polinomi di Schur shifted-simmetrici è stato studiato da Okounkov in una serie lavori, tramite la nozione di immanante quantico. Gli immananti quantici sono elementi di ζ(n) assai difficilmente trattabili, come commentato dallo stesso Okounkov. Si è sviluppata una teoria sistematica degli immananti quantici e del centro ζ(n) basata sulla nuova nozione di immanante di Capelli in U(gl(n)). Gli immananti di Capelli sono una generalizzazione sia degli immananti classici (Littlewood/Richardson, 1934) di una matrice ad entries commutativi, sia del celebre determinante di Capelli in U(gl(n)), sono efficacemente trattabili, e formano un sistema di generatori lineari (compatibili con la filtrazione naturale di U(gl(n)). Gli immananti quantici di Okounkov risultano semplici combinazioni lineari di immananti di Capelli. ll passaggio al limite n→ ∞ per ζ(n) e ∧∗(n) si descrive esplicitamente come limite diretto rispetto alla decomposizione/proiezione Olshanski.

04
Apr

2019
Stefano Biagi
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

Maximum Principles on unbounded domains play a crucial role in several problems related to linear second-order PDEs of elliptic and parabolic type. In this seminar we consider a class of sub-elliptic operators L in R^N and we establish some criteria for an unbounded open set to be a Maximum Principle set for L.

02
Apr

2019
Alessandro D'Andrea
Algebre di Lie linearmente compatte e pseudoalgebre di Lie

seminario di algebra e geometria

Presenterò brevemente la teoria delle algebre di Lie linearmente compatte, ricordando la classificazione delle strutture semplici e delle loro rappresentazioni irriducibili discrete. Introdurrò poi le pseudoalgebre di Lie (possibilmente super) spiegando come queste strutture solo legate alle (super)algebre di Lie linearmente compatte e reinterpretando la teoria della rappresentazione in termini del complesso di de Rham e di alcune sue generalizzazioni.

02
Apr

2019
Gavarini
Twisted deformations vs. cocycle deformations for quantum groups

seminario di algebra e geometria

We study two deformation procedures for quantum groups — namely, quantum universal enveloping algebras — those realized as twist deformations (that modify the coalgebra structure, while keeping the algebra one), called “twisted quantum groups” (=TwQGp’s), and those realized as 2–cocycle deformations (that deform the algebra structure, but save the coalgebra one), called “multiparameter quantum groups” (=MpQG’s). Up to technicalities, we show that the two methods actually are equivalent, in that they eventually provide isomorphic outputs.

02
Apr

2019
Prof. F. Gavarini
Twisted deformations vs. cocycle deformations for quantum groups

seminario di algebra e geometria

We study two deformation procedures for quantum groups — namely, quantum universal enveloping algebras — those realized as twist deformations (that modify the coalgebra structure, while keeping the algebra one), called “twisted quantum groups” (=TwQGp’s), and those realized as 2–cocycle deformations (that deform the algebra structure, but save the coalgebra one), called “multiparameter quantum groups” (=MpQG’s). Up to technicalities, we show that the two methods actually are equivalent, in that they eventually provide isomorphic outputs.

02
Apr

2019
Prof. F. Gavarini
Twisted deformations vs. cocycle deformations for quantum groups

seminario di algebra e geometria

We study two deformation procedures for quantum groups — namely, quantum universal enveloping algebras — those realized as twist deformations (that modify the coalgebra structure, while keeping the algebra one), called “twisted quantum groups” (=TwQGp’s), and those realized as 2–cocycle deformations (that deform the algebra structure, but save the coalgebra one), called “multiparameter quantum groups” (=MpQG’s). Up to technicalities, we show that the two methods actually are equivalent, in that they eventually provide isomorphic outputs.

01
Apr

2019
Marco Alessandro Fuhrman
An introduction to optimal switching problems

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

Il seminario si pone lo scopo di presentare il problema di switching (commutazione) ottimale e alcune delle tecniche per risolverlo, sia quelle più classiche sia altre che sono state introdotte solo recentemente. Inizialmente verrà formulato il problema per un'equazione differenziale stocastica controllata, governata dal moto Browniano. Si considererà dapprima l'approccio basato sulla programmazione dinamica e le equazioni di Hamilton-Jacobi-Bellman, che in questo caso costituiscono un sistema di equazioni differenziali a derivate parziali accoppiate per mezzo di una condizione di ostacolo. In seguito si passerà a considerare una tecnica più probabilistica basata sulle equazioni differenziali stocastiche "backward": anche in questo caso si tratta di un sistema con condizioni di riflessione. Verrà presentato anche un approccio alternativo basato su una singola equazione con un vincolo di tipo differente. La presentazione sarà di tipo pedagogico ma avanzata. In particolare il problema di arresto ottimale verrà presentato come un caso più semplice per introdurre il caso di switching generale.

29
Mar

2019
Lothar Reichel
Tikhonov regularization, GMRES, and preconditioning for linear discrete ill-posed problems

seminario di analisi numerica

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as boundary value problems for elliptic partial differential equations. The method is also applied to the iterative solution of linear systems of equations that are obtained by discretizing linear ill-posed problems, such as many inverse problems. However, GMRES does not always perform well when applied to the latter kind of problems. This talk seeks to shed some light on reasons for the poor performance of GMRES in certain situations, and discusses some remedies based on specific kinds of preconditioning. The standard implementation of GMRES is based on the Arnoldi process, which also can be used to define a solution subspace for Tikhonov or TSVD regularization, giving rise to the Arnoldi-Tikhonov and Arnoldi-TSVD methods, respectively. The performance of the GMRES and the latter methods is discussed.

28
Mar

2019
Mirella Manaresi (Università di Bologna)
Paolo Salmon a Bologna

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario interdisciplinare

28
Mar

2019
Claudio Pedrini (Università di Genova)
La "crisi" della geometria algebrica in Italia e l’algebra commutativa: l'attività scientifica di Paolo Salmon a Genova

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario di algebra e geometria

28
Mar

2019
Carlo Traverso (Università di Pisa)
Seminormalità e gruppo di Picard

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario di algebra e geometria

28
Mar

2019
Silvio Greco (Politecnico di Torino)
Paolo Salmon a Pisa: l'esordio di un maestro

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario di algebra e geometria

28
Mar

2019
Paolo Valabrega (Politecnico di Torino)
Paolo Salmon, un matematico e un amico

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario interdisciplinare

28
Mar

2019
Claudio Procesi (Università Roma La Sapienza)
L'ALGEBRA IN ITALIA NEGLI ANNI '60

nel ciclo di seminari: PAOLO SALMON E L'ALGEBRA COMMUTATIVA IN ITALIA

seminario di algebra e geometria

27
Mar

2019
Marco Viola

seminario di analisi numerica

Gradient projection (GP) methods have proved to be very efficient in the solution of optimization problems in which the projection onto the feasible set can be computed cheaply. In this seminar we, at first, review the theoretical results and algorithmic techniques developed for the case of bound constrained quadratic programming problems (BQPs). Then, we propose a gradient-based framework, called "Proportionality-based Subspace Accelerated framework for Quadratic Programming" (PSAQP), for quadratic programming problems. Inspired by the gradient projection conjugate gradient (GPCG) algorithm for convex BQPs [J. J. Moré and G. Toraldo, SIAM J. Optim., 1 (1991), pp. 93{113], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations until either a candidate active set is identified or no reasonable progress is made, and an unconstrained minimization phase, which reduces the objective function in a suitable space defined by the identification phase. The proposed framework differs from GPCG not only because it deals with a more general class of problems, but mainly for the way it stops the minimization phase. Indeed, thanks to a component-wise reformulation of the first-order KKT conditions, we introduce a way to estimate the Lagrange multipliers which is exploited to formulate an efficient criterion to switch between the two phases. If the objective function is bounded, every method fitting in the framework converges to a stationary point thanks to a suitable application of the GP method in the identification phase. For strictly convex problems, finite convergence is proved even in the case of degeneracy of the solution. Numerical experiments show that practical algorithms in this framework are competitive with reference algorithms for the solution of synthetic and real-life problems subject to bounds only or to bounds and a single linear constraint.

27
Mar

2019
Silvia Benvenuti
Tips for science communication

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

È matematicamente certo. Fate l’ipotesi che voi siate matematici e il vostro partner sia, per esempio, neurochirurgo. Vi presentate a cena, con un gruppo di nuovi amici. Fate quattro chiacchiere e dopo un po’ viene fuori che siete un ricercatore in matematica. Un attimo di sconcerto, sguardi di divertito stupore, e poi vi chiedono: «ma perché, cosa c'è da ricercare, in matematica?» Guardandosi tra loro, insistono: «non è già tutto scoperto?» E sicuramente almeno uno affermerà, con orgoglio: «io, la matematica, non l'ho mai capita!» Ma il peggio è che, mentre voi cercate di spiegare cosa mai giustifichi il vostro, peraltro misero, stipendio, i commensali scopriranno la professione del vostro partner. Fine dei vostri tre minuti di protagonismo: con sguardo stavolta sognante, il vicino di tavola si rivolgerà alla vostra metà, innanzi tutto convinto di essere in grado di intavolare una conversazione su argomenti di comune interesse, poi mentalmente calcolando il suo stipendio assolutamente rispettabile, per poi perdersi definitivamente dietro al fascino che il camice bianco evoca nella mente di chiunque. Voi scomparirete inesorabilmente, a far compagnia a ricordi tendenzialmente sgradevoli di numeri, equazioni, formule e simili inutilità. Insomma, nell'immaginario comune, il medico è un’attrazione, il matematico è un nerd. Sottili varianti si possono ottenere sostituendo a vostro piacimento "neurochirurgo" con “ingegnere elettronico", "magistrato", "architetto", "promotore finanziario", "biologo marino" e, addirittura, "fisico". C’è poco da fare, esiste un problema di rappresentazione della matematica e dei matematici nell’immaginario popolare, ed è un problema serio. In questo seminario ci proponiamo di chiarirne i termini, provando anche a esplorare possibili soluzioni. Purtroppo, anche alla fine di questa chiacchierata, non sarà ancora chiaro se queste esistano: in caso positivo, però, sappiamo già che certamente non saranno uniche!

26
Mar

2019
Vladimir Druskin, Mathematical Sciences Dept, Worcester Polytechnic Institute, MA (USA)
Embedding properties of network realizations of reduced order models with applications to inverse scattering and data science

seminario di analisi numerica

26
Mar

2019
Dennis The
Symmetry gaps for geometric structures

seminario di algebra e geometria

For a given type of differential geometric structure, there is often a gap between the maximal and "submaximal" infinitesimal symmetry dimensions. This was first observed in the 19th century for Riemannian metrics and such symmetry gaps were subsequently classified for various other geometric structures on a case-by-case basis. I will describe joint work with Boris Kruglikov that gave a uniform approach to the symmetry gap problem for the class of parabolic geometries. This is a diverse class of geometric structures that include conformal, projective, CR, 2nd order ODE systems, and large classes of generic distributions. A priori, submaximally symmetric structures need not even be homogeneous, but remarkably, in many cases this geometric problem reduces ultimately to Dynkin diagram combinatorics, and some submaximally symmetric models can be "immediately" found (in a sense that I will make precise).

26
Mar

2019
Claudio Procesi
Perpetuants: a lost treasure

seminario di algebra e geometria

Perpetuant is one of the several concepts invented (in 1882) by J. J. Sylvester in his investigations of covariants for binary forms. It appears in one of the first issues of the American Journal of Mathematics which he had founded a few years before. It is a name which will hardly appear in a mathematical paper of the last 70 years, due to the complex history of invariant theory which was at some time declared dead only to resurrect several decades later. I learned of this word from Gian-Carlo Rota who pronounced it with an enigmatic smile. In this talk I want to explain the concept, a Theorem of Stroh, and some new explicit description.

25
Mar

2019
Andrea Santi
On the BBW theorem

seminario di algebra e geometria

TBA

25
Mar

2019
Lothar Reichel
Title: The Arnoldi decomposition, Tikhonov regularization, GMRES, and preconditioning for linear discrete ill-posed problems

seminario di analisi numerica

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as boundary value problems for elliptic partial differential equations. The method is also applied to the iterative solution of linear systems of equations that are obtained by discretizing linear ill-posed problems, such as many inverse problems. However, GMRES does not always perform well when applied to the latter kind of problems. This talk seeks to shed some light on reasons for the poor performance of GMRES in certain situations, and discusses some remedies based on specific kinds of preconditioning. The standard implementation of GMRES is based on the Arnoldi process, which also can be used to define a solution subspace for Tikhonov or TSVD regularization, giving rise to the Arnoldi-Tikhonov and Arnoldi-TSVD methods, respectively. The performance of the GMRES and the latter methods is discussed. This talk presents joint work with Silvia Gazzola, Silvia Noschese, Paolo Novati, and Ronny Ramlau.

22
Mar

2019
Dennis The
Homogeneous Levi non-degenerate hypersurfaces in C3

seminario di algebra e geometria

TBA

22
Mar

2019
Pietro Rigo
On the existence of continuous processes with given one-dimensional distribution

seminario di probabilità

Let $\mathcal{P}$ be the collection of Borel probability measures on $\mathbb{R}$, equipped with the weak* topology, and let $\mu:[0,1]\rightarrow\mathcal{P}$ be a continuous map. Say that $\mu$ is presentable if $X_t\sim\mu_t$, $t\in [0,1]$, for some real process $X$ with continuous paths. It may be that $\mu$ fails to be presentable. Conditions for presentability are given in this note. For instance, $\mu$ is presentable if $\mu_t$ is supported by an interval for all but countably many $t$. In addition, assuming $\mu$ presentable, we investigate whether there is a continuous process $X$ with the same finite dimensional distributions as the quantile process $Q$ induced by $\mu$. The latter is defined, on the probability space $((0,1),\mathcal{B}(0,1),\,$Lebesgue measure$)$, by \begin{gather*} Q_t(\alpha)=\inf\,\bigl\{x\in\mathbb{R}:\mu_t(-\infty,x]\ge\alpha\bigl\}\quad\quad\text{for all }t\in [0,1]\text{ and }\alpha\in (0,1). \end{gather*} Various open problems are stated as well.

22
Mar

2019
Paolo Dai Pra
Thermodynamic limit and phase transitions in non-cooperative games: some mean-ﬁeld examples

nell'ambito della serie: SEMINARI DI PROBABILITÀ E STATISTICA MATEMATICA

seminario di probabilità

In stochastic dynamics inspired by Statistical Mechanics the interaction between diﬀerent particles, or agents, is usually expressed as a given function of their states. The behavior of the system, in the limit of inﬁnitely many particles (thermodynamic limit), may change dramatically by small changes in the parameters of the model: when this occurs we say there is a phase transition. In many applications the interaction cannot be given a priori but it is rather a result of agents’ strategy, aimed at optimizing a given performance. Using the simplest models of this nature, mean ﬁeld games, we illustrate some examples of phase transitions, pointing to diﬃculties in the proof of the thermodynamic limit.

21
Mar

2019
Antonio Vitolo, Università di Salerno
Maximum principles with low ellipticity

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

19
Mar

2019
Antonio Rapagnetta
A class of examples of singular irreducible symplectic varieties.

nel ciclo di seminari: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

By the Bogomolov decomposition theorem, irreducible holomorphic symplectic manifolds play a central role in the classification of compact Kähler manifolds with numerically trivial canonical bundle. Very recently, Höring and Peternell completed the proof of the existence of a singular analogue of the Bogomolov decomposition theorem. In view of this result, singular irreducible symplectic varieties (following Greb, Kebekus and Peternell) are singular analogue of irreducible holomorphic symplectic manifolds. In a joint work with Arvid Perego, still in progress, we show that all moduli spaces of sheaves on projective K3 surfaces are singular irreducible symplectic varieties. We compute their Beauville form and the Hodge decomposition of their second integral cohomology, generalizing previous results, in the smooth case, due to Mukai, O'Grady and Yoshioka.

13
Mar

2019
Luca Moci
A gentle introduction to matroids

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

Matroids axiomatise the notion of linear dependence for a list of vectors. While the applications to computer science and optimization are known since long time, surprising interactions of matroid theory with algebra and algebraic geometry were recently discovered, leading to the proof of important combinatorial conjectures and to the introduction of new matroids invariants. In the first part of the talk I will give an elementary introduction to the topic, focusing on examples arising from graphs and from families of hyperplanes in a vector space.​ In the second part of the talk I will show that the set of (isomorphism classes of) matroids has a natural structure of Hopf algebra. Then I will introduce a class of matroid-like objects, called minor systems, and describe the related bialgebras. This machinery allows to give rise to a wide number of invariants, old and new. (Partially based on joint work with Alex Fink and Clement Dupont)

13
Mar

2019
Stefano Pagliarani - DIES, Università di Udine
Fixed-point theorems and Picard iteration methods for McKean-Vlasov mean-field SDEs with jumps

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

We consider a prototype class of Lévy-driven SDEs with McKean-Vlasov (mean-field) interaction in the drift. The coefficient is assumed to be affine in the state-variable and only measurable in the law. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration method that approximates the law of the solution. Numerical illustrations show the effectiveness of the method, which appears to be appropriate to handle multi-dimensional settings. We finally describe possible extensions and generalizations to more general settings. This talk is based on joint work with Ankush Agarwal.

12
Mar

2019
Roberto Pagaria
Toric arrangements: an introduction between Algebra, Topology and Combinatorics

seminario di algebra e geometria

In the first part, we will introduce the theory of hyperplane arrangements with particular attention to the cohomology algebra of the complement of the arrangement. The talk will start from the basic definitions of the topological and combinatorial objects involved. We will exhibit the connections between hyperplane arrangements and other branch oh Mathematics, e.g. knot theory and graph theory. The second part will focus on toric arrangements, a generalization of hyperplane arrangements. We will give a presentation of the cohomology algebra of the complement of a toric arrangement (this is a joint work with F. Callegaro, M. D'Adderio, E. Delucchi, and L. Migliorini) and we will discuss its dependency on the combinatorial data of the arrangement.

12
Mar

2019
Roberto Pagaria
TBA

seminario di algebra e geometria

12
Mar

2019
Elena Bandini (Università degli Studi di Milano-Bicocca)
BSDEs driven by a general random measure and optimal control for piecewise deterministic Markov processes

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

We consider an optimal control problem for piecewise deterministic Markov processes (PDMP) on a bounded state space. Here a pair of controls acts continuously on the deterministic flow and on the transition measure describing the jump dynamics of the process. For this class of control problems, the value function can be characterized as the unique viscosity solution to the corresponding integro-differential Hamilton-Jacobi-Bellman equation with a non-local type boundary condition. We are able to provide a probabilistic representation for the value function in terms of a suitable backward stochastic differential equation, known as nonlinear Feynman-Kac formula. The jump mechanism from the boundary entails the presence of predictable jumps in the PDMP dynamics, so that the associated BSDE turns out to be driven by a random measure with predictable jumps. Existence and uniqueness results for such a class of equations are non-trivial and are related to recent works on well-posedness for BSDEs driven by non quasi-left-continuous random measures.

08
Mar

2019
Hirokazu Tanaka
Computational modeling of the motor cortex and the cerebellum

nel ciclo di seminari: NEUROMATEMATICA

seminario interdisciplinare

This talk summarizes two modeling studies on the motor cortex and the cerebellum. The motor cortex is the final cortical pathway to motor circuits in the spinal cord, but its functional role has long been debated, particularly whether the motor cortex represents movement kinematics or dynamics. To resolve this issue, I modeled the visuomotor transformation using Newton-Euler equations of motion that has been used in robotics, and proposed that neural activities in the motor cortex represent vector cross products in the equations. This model explains a wide variety of the characteristics reported in the motor cortex in a unified manner. The cerebellum is hypothesized to predict a future state of the body from a current state and a corollary discharge, the computation known as an internal forward model. Although this hypothesis has been supported from a number of clinical, psychophysical and neuroimaging studies, a direct neurophysiological evidence is missing. I analyzed firing rates of mossy fibers (cerebellar inputs), Purkinje cells (outputs from cerebellar cortex), and dentate cells (cerebellar outputs) recorded from a behaving monkey. I found that the cerebellar outputs provided predictive information about future inputs to the cerebellum, providing direct neurophysiological evidence for the forward-model hypothesis of the cerebellum. [1] Tanaka, H., & Sejnowski, T. J. (2013). Computing reaching dynamics in motor cortex with Cartesian spatial coordinates. Journal of Neurophysiology, 109(4), 1182-1201. [2] Tanaka, H., & Sejnowski, T. J. (2015). Motor adaptation and generalization of reaching movements using motor primitives based on spatial coordinates. Journal of Neurophysiology, 113(4), 1217-1233. [3] Tanaka, H., Ishikawa, T., & Kakei, S. (2019). Neural Evidence of the Cerebellum as a State Predictor. The Cerebellum, 1-23.

08
Mar

2019
Fausto Gozzi
Viscosity solutions for PDEs on Wasserstein space

seminario di probabilità

07
Mar

2019
Huyên Pham
McKean-Vlasov stochastic optimal control problem

seminario di probabilità

07
Mar

2019
Idris Kharroubi
Quenched mass transport of particles towards a target

seminario di probabilità

06
Mar

2019
Andrea Cosso
McKean-Vlasov stochastic control and Hamilton-Jacobi-Bellman equations on Wasserstein space

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di probabilità

06
Mar

2019
Fabrizio Lillo
An introduction to market impact modeling and optimal execution in financial markets

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

Market impact is the response of prices to trades and is a fundamental quantity to understand how supply and demand affect price, but also an important component of transaction costs. In this talk, I introduce the still open problem of mathematical modeling of market impact in a way which is consistent with data but also lacking dynamical arbitrage opportunities. I review some models proposed in the mathematical finance literature and discuss their comparison with data, deriving necessary conditions for the absence of dynamical arbitrage. I then focus on the optimal execution problem in continuous and discrete time, deriving the solution under different specifications of the impact model and of the chosen benchmark.

05
Mar

2019
Dominik Garmatter
"Penalty formulations for mixed integer and PDE constrained optimization problems"

seminario di analisi numerica

Seminario nell'ambito del progetto MIUR-DAAD 2018-2020, Universita- di Bologna e TU-Chemnitz

05
Mar

2019
Davide Bolognini
Results and problems in Algebraic Combinatorics

seminario di algebra e geometria

In the first part of the seminar, I recall some basic definitions from Commutative Algebra and Combinatorics. In particular, I consider classes of homogeneous ideals arising from discrete structures. The main goal of my research is to describe algebraic properties of these ideals in combinatorial terms. A typical example of this approach is to establish relations between the graded Betti numbers of monomial ideals and the structure of associated simplicial complexes or hypergraphs. In this flavour, I present various results, suggesting also possible future developments. Time permitting, in the last part of the seminar I focus on new directions of research, involving arithmetic matroids and a generalization of flag varieties.

04
Mar

2019
Piergiacomo Sabino (Uniper Global Commodities SE, Dusseldorf)
Forward or backward simulation? A comparative study

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

The aim of this study is to present algorithms for the backward simulation of standard processes that are commonly used in financial applications. We extend the works of Ribeiro and Webber and Avramidis and L’Ecuyer on gamma bridge and obtain the backward construction of a Gamma process. Moreover, we are able to write a novel acceptance-rejection algorithm to simulate Inverse Gaussian (IG) processes backward in time. Therefore, using the time-change approach, we can easily get the backward generation of the Compound Poisson with infinitely divisible jumps, the Variance–Gamma the Normal–Inverse–Gaussian processes and then the time-changed version of the OU process (SubOU) introduced by Li and Linetsky. We then compare the computational costs of the sequential and backward path generation of such processes and show the advantages of adopting the latter one, in particular in the context of pricing American options or energy facilities like gas storages.

28
Feb

2019
Claudia Bucur, Università Cattolica del Sacro Cuore
Behaviour of nonlocal sets for small values of the fractional parameter

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

seminario di analisi matematica

28
Feb

2019
Paolo Pigato (Weierstrass Institute for Applied Analysis and Stochastics, Berlino)
Density and tube estimates for diffusion processes under Hormander-type conditions

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

We recall some classic results on the regularity of solutions of stochastic differential equations. Then we consider two specific diffusion processes satisfying hypoellipticity conditions of Hormander type. Using Malliavin Calculus techniques recently developed to deal with degenerate problems, we find estimates for the density of the law of the solution, which we use to prove exponential bounds for the probability that the diffusion remains in a small tube, around a deterministic path, up to a given time. We then present some work in progress on asymptotic sharp estimates for the density and its derivatives for a similar, higher dimensional system.

27
Feb

2019
Vittorio Martino
Introduction to minimax methods

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

We will introduce the basic tools for the topological methods in critical points theory: the Palais-Smale compactness condition and the deformation lemma. Starting from the finite dimensional case, we will illustrate how the minimax argument works. Eventually, we will show some applications to problems in infinite dimensional setting.

26
Feb

2019
Claudio Onorati
The monodromy group of IHS manifolds of OG10-type

nel ciclo di seminari: SEMINARIO DI ALGEBRA E GEOMETRIA

seminario di algebra e geometria

The monodromy group of an IHS manifold is one of the most important tools to investigate their geometry. In the first part of the talk, I will recall the main definitions, giving some motivation. In the second half I will focus on the OG10-type. This is the only type (among the known ones) for which the monodromy group is still a mystery. We explain how to construct new monodromy operators using two families, the O'Grady and the Laza-Saccà-Voisin ones, exhibiting an explicit subgroup of the monodromy group, that we conjecture being all. Time permitting, we will also discuss a geometric constraint to the fact that the monodromy group is smaller than the group of orientation preserving isometries.

20
Feb

2019
Annalisa Panati, Centre de Physique Théorique, Luminy et Université de Toulon.
Heat fluctuations in the two-time measurement framework and ultraviolet regularity

seminario di fisica matematica

Since Kurchan’s seminal work (2000), two-time measurement statistics (also known as full counting statistics) has been shown to have an important theoretical role in the context of quantum statistical mechanics, as they allow for an extension of the celebrated fluctuation relation to the quantum setting. In this contribution, we consider two-time measurement statistics of heat for a locally perturbed system, and we show that the description of heat fluctuation differs considerably from its classical counterpart, in particular a crucial role is played by ultraviolet regularity conditions. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0. On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation. This phenomenon has no classical analogue.

19
Feb

2019
Luca Sabatini
Random Walks in Finite Groups

seminario di algebra e geometria

As the name declares, the theory of random walks in groups is somehow in the middle of group theory and probability theory. The central question is “how to generate a group efficiently?” In this seminar I will present the notions of diameter, mixing time and expander graphs, as well as some explicit constructions. The second part will be dedicated to the Bourgain-Gamburd Machine, a recent technique to show expansion in quasirandom groups.

18
Feb

2019
Alessandro Gimigliano
Tensor decomposition and secant varieties

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

Determining secant varieties (i.e. varieties which are the union of secant lines, planes, etc.) for a given projective variety X is a classical problem in Algebraic Geometry. When X is a Segre Variety, its secant varieties parameterize tensors with assigned tensor rank, and their study is related to the study of tensor decompositions, a quite relevant issue in applied math. In a similar way, secant varieties of Veronese varieties are related to symmetric tensors. In this talk a sketchy view of the state of the art on these problems will be given.

15
Feb

2019
Alessandro Della Corte (Sapienza Università di Roma)
The Kolakoski sequence: open problems and new approaches

seminario di fisica matematica

The Kolakoski sequence S is the unique sequence on the alphabet {1,2} starting with 1 and coinciding with its own run length encoding: S = 122112122122112… The (few) known properties and the open problems concerning S will be described and some new approaches will be proposed.

15
Feb

2019
Vit Tucek
BGG sequences from infinite-rank bundles

seminario di algebra e geometria

I will present a generalization of Calderbank-Diemer construction that works for bundles whose fiber is unitarizable highest weight module. These modules exists only when $(G, K)$ is Hermitian symmetric pair. The resulting BGG sequences of Verma modules are (after a twist) generalizations of minimal free resolutions of determinantal ideals. This suggests that these sequences of differential operators are in fact resolutions for interesting differential operators such as Yamabe or Dirac on $G^\mathb{C}/P$. Moreover these differential operators still obey $A_\infty$ relations as in the classical case of finite-dimensional bundles.

15
Feb

2019
Matthias Hammerl
Parabolic geometries: Overdetermined differential equations, holonomy reductions and compactifications/ Part 2

seminario di algebra e geometria

Parabolic geometries provide a uniform framework to describe, treat and analyse a number of differential geometric structures, most prominently projective structures, conformal structures & CR-structures. I will give an introduction to the most important features of parabolic geometries, most importantly in the area of conformal (spin) structures and how this framework can be used to treat interesting geometric differential equations via the BGG-machinery. A major advance in this area was a uniform holonomy reduction theorem, known as 'curved orbit decompositions'. I will explain via some examples how curved orbit decompositions can be used to understand the geometric implications of the existence of solutions to BGG-equations and in particular sheds light on 'singularity sets'. A final topic of this talk will be compactifications of parabolic geometries which are again intimately related with the concept of holonomy reductions and curved orbit decompositions.

15
Feb

2019
Huerta
Division algebras and the brane bouquet

nel ciclo di seminari: JOHN HUERTA

seminario di algebra e geometria

In the last talk, we met some "higher" algebraic structures associated to strings. We expand on this idea, to give the Fiorenza-Sat-Schreiber "brane bouquet" of L-infinity algebras. Then we describe our most recent work with Sati and Schreiber: in the 11 dimensional spacetime famous from supergravity and M-theory, we review the classification of finite group actions that preserve some supersymmetry, and show how we can extend the brane bouquet to this equivariant setting.

14
Feb

2019
Vit Tucek
Representation theory and BGG

seminario di algebra e geometria

We discuss the link between representation theory and invariant operators

14
Feb

2019
Matthias Hammerl
Parabolic geometries: Overdetermined differential equations, holonomy reductions and compactifications

seminario di algebra e geometria

Parabolic geometries provide a uniform framework to describe, treat and analyse a number of differential geometric structures, most prominently projective structures, conformal structures & CR-structures. I will give an introduction to the most important features of parabolic geometries, most importantly in the area of conformal (spin) structures and how this framework can be used to treat interesting geometric differential equations via the BGG-machinery. A major advance in this area was a uniform holonomy reduction theorem, known as 'curved orbit decompositions'. I will explain via some examples how curved orbit decompositions can be used to understand the geometric implications of the existence of solutions to BGG-equations and in particular sheds light on 'singularity sets'. A final topic of this talk will be compactifications of parabolic geometries which are again intimately related with the concept of holonomy reductions and curved orbit decompositions.

14
Feb

2019
Dmitri Alekseevsky
Homogeneous sub-Riemannian manifolds, part 1

seminario di algebra e geometria

There are many equivalent definitions of Riemannian geodesics The definitions can be divided into two classes : geodesics as "shortest curves defined by a variational principle, and geodesics as "straightest curves defined by a connection. All definitions are naturally generalised to sub-Riemannian manifolds, but become non-equivalent. A. Vershik and L. Faddeev showed that for a generic sub-Riemannian manifold (Q, D, g) shortest geodesics ( used in control theory) are different from straightest geodesics (used in non-holonomic mechanics)) on a open dense submanifold. They gave first example (compact Lie group with the bi-invariant metric) when shortest geodesics coincides with straightest geodesics and stated the problem to describe more general class of sub-Riemannian manifolds with this property . We generalised the Vershik-Faddeev example and consider a big class of sub-Riemannian manifolds associated with principal bundle over a Riemannian manifolds, for which shortest geodesics coincides with straightest geodesics. Using the geometry of flag manifolds, we describe some classes of compact homogeneous sub-Riemannian manifolds ( including contact sub-Riemannian manifolds and symmetric sub-Riemannian manifolds ) where straightest geodesics coincides with shortest geodesics. Construction of geodesics in these cases reduces to description of Riemannian geodesics of the Riemannian homogeneous manifold or left-invariant metric on a Lie group.

14
Feb

2019
Antonio Ricciardo
Super Jordan triple systems

seminario di algebra e geometria

In this seminar we will introduce the supersymmetric Jordan triple systems: a new algebraic structure which generalizes the class of Jordan triple systems as well as the class of N=6 3-algebras. We will describe their relation with graded Lie superalgebras with involutions via the Tits-Kantor-Koecher construction. Their classification, obtained via the TKK construction, will be discussed and the explicit realizations of the systems related to the special and to the exceptional Lie superalgebras will be given. The infinite-dimensional linearly-compact case will also be presented.

14
Feb

2019
Huerta
Division algebras and supersymmetry

nel ciclo di seminari: JOHN HUERTA

seminario di algebra e geometria

Abstract: In this introduction suitable for graduate students, we use the four normed division algebras to introduce some basic elements of supersymmetry. Namely, from the four normed division algebras (the real numbers, the complex numbers, the quaternions and the octonions), a uniform construction yields the super-Minkowski spacetimes on which the classical superstring can be defined. We review this construction and show how the alternativity of the division algebras allows us to define a class in the third cohomology on super-Minkowski spacetime, which in turn allows us to write the classical action of the superstring. In conclusion, we describe how this degree three class defines a "higher" algebraic structure.

14
Feb

2019
Roberto Catenacci
Forms in Supergeometry, part 1

seminario di fisica matematica

I will review the theory of superforms, integral forms and inverse forms in supermanifolds from a sheaf-theoretical point of view.. The formal "distributional" properties of forms and of Picture Changing Operators in superstring field theory are recovered geometrically, providing a mathematical foundation for the concept of Large Hilbert Space. Finally, I will discuss a new A-infinity algebra structure emerging (more or less naturally...) on supermanifolds.

06
Feb

2019
Sabino Di Trani
Lie groups and combinatorics of the exterior algebra.

seminario di algebra e geometria

Let G be a simple Lie group over C and let Lie(G) be its Lie algebra. The exterior algebra of Lie(G) is extensively studied in literature for its link with the geometry of G and the combinatorics of the Weyl group W(G). In this talk I will present an overview of some classical results about the exterior algebra in a "representation theory"-flavour, with a particular attention to two open conjectures due to Kostant and Reeder.

06
Feb

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 6/6
See https://phd.unibo.it/matematica/it/didattica/2018-2019

06
Feb

2019
Giovanni Luca Torrisi
The Clark-Ocone formula and the Poincare' inequality for point processes

nel ciclo di seminari: SEMINARI DI PROBABILITÀ

seminario di probabilità

Clark-Ocone formulas are powerful results in stochastic analysis with a variety of applications. In the talk we provide the Clark-Ocone formula for square-integrable functionals of point processes with stochastic intensity. Then we present two applications of the formula: the Poincare' inequality and a concentration bound for those functionals. Our results generalize the corresponding ones on the Poisson space. The talk is based on joint works with Ian Flint and Nicolas Privault (NTU, Singapore)

05
Feb

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 5/6

seminario di analisi matematica

See https://phd.unibo.it/matematica/it/didattica/2018-2019

01
Feb

2019
Enrico Fatighenti
Fano varieties of K3 type and IHS manifolds

seminario di algebra e geometria

Subvarieties of Grassmannians (and especially Fano varieties) obtained from section of homogeneous vector bundles are far from being classified. A case of particular interest is given by the Fano varieties of K3 type, for their deep links with hyperk\"ahler geometry. This talk will be mainly devoted to the construction of some new examples of such varieties. This is a work in progress with Giovanni Mongardi.

30
Gen

2019
Claudio Bonanno (Università di Pisa)
Zero Entropy: Mathematics and Applications

seminario di fisica matematica

One of the mathematical definitions of "chaos" is given in terms of the measure-theoretic (or metric, or Kolmogorov) entropy, and chaotic dynamical systems are often defined to be systems with positive entropy. However many systems with a "chaotic" behaviour have zero entropy, and the same is true for some time series of the real world. In this talk I will first introduce the notion of zero entropy systems and some examples. Then I will show how these systems represent an interesting challenge from the mathematical point of view, as many results from Dynamical Systems Theory do not hold, and some definitions are hard to be extended to these systems.

30
Gen

2019
Enrico Rogora
Il Liceo Matematico e l’esperienza dei Laboratori Interdisciplinari

seminario interdisciplinare

Nel seminario verrà presentato il progetto nazionale del Liceo Matematico: l’organizzazione generale, gli aspetti condivisi che accomunano le diverse esperienze locali e le criticità emerse nei primi due anni di sperimentazione. Verrano successivamente trattati alcuni aspetti specifici della realtà romana, in particolare quelli che riguardano la progettazione e la realizzazione dei laboratori interdisciplinari sull’educazione allo sguardo, sull’educazione all’argomentazione e sull’educazione al pensiero probabilistico.

30
Gen

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 4/6

seminario di analisi matematica

See https://phd.unibo.it/matematica/it/didattica/2018-2019

30
Gen

2019
Nicolas Macris
Error correcting codes, machine learning and the Nishimori line.

seminario di fisica matematica

29
Gen

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 3/6

seminario di analisi matematica

See https://phd.unibo.it/matematica/it/didattica/2018-2019

29
Gen

2019
Nicolas Gillis
Linear dimensionality reduction for data analysis

28
Gen

2019
Alessandro Sarti
The differential brain: from neurogeometry to heterogenesis

seminario interdisciplinare

28
Gen

2019
Nicolas Macris
Optimal errors and phase transitions in high-dimensional generalized linear models

seminario interdisciplinare

Generalized linear models arise in high-dimensional machine learning, statistics, communications and signal processing. In this talk we review such models in a teacher-student setting of supervised learning, and when the data matrix is random, as relevant in benchmark models of neural networks. Predictions for the mutual information and Bayes-optimal generalization errors have existed since a long time for special cases, e.g. for the perceptron or the committee machine, in the field of statistical physics based on spin-glass methods. We will explain recently developed mathematical techniques rigorously establishing those old conjectures and bring forward their algorithmic interpretation in terms of performance of message-passing algorithms. For many learning problems, we will illustrate regions of parameters for which message passing algorithms achieve the optimal performance, and locate the associated sharp phase transitions separating learnable and non-learnable regions. These rigorous results can serve as a challenging benchmark for multi-purpose algorithms.

28
Gen

2019
philipp grohs
Approximation theory, Numerical Analysis and Deep Learning

seminario interdisciplinare

28
Gen

2019
Ernesto De Vito
Supervised learning theory: a mathematical review

seminario interdisciplinare

In this talk I give an introduction to the mathematical framework of supervised learning theory, emphasizing the connection with other fields of mathematics and underlining some open problems.

26
Gen

2019
M. Bonforte
TBA

nel ciclo di seminari: GHAIA MEETING

seminario di analisi matematica

26
Gen

2019
Blanca Ayuso
Unfitted Nitsche methods of high contrast interface elliptic problems: methods and simple preconditioners

nel ciclo di seminari: GHAIA MEETING

seminario di analisi numerica

26
Gen

2019
Manuel Ritoré
Isoperimetric inequalities in unbounded convex bodies

nel ciclo di seminari: GHAIA MEETING

seminario di analisi matematica

e consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body in Euclidean space, without assuming any regularity on its boundary. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict concavity of the isoperimetric profile and, consequently, the connectedness of generalized isoperimetric regions. We also focus on the cases of small as well as of large volumes; in particular we show existence of isoperimetric regions with sufficiently large volumes, for special classes of unbounded convex bodies. We finally address some questions about isoperimetric rigidity and analyze the asymptotic behavior of the isoperimetric profile in connection with the notion of isoperimetric dimension. This is joint work with Gian Paolo Leonardi and Efstratios Vernadakis.

25
Gen

2019
prof. M. Ritoré
partecipazione a meeting di progetto

nel ciclo di seminari: GHAIA MEETING

seminario interdisciplinare

presentazione dei risultati raggiunti nel WP4. Il seminario è aperto solo ai membri del progetto. Si svolge alla presenza dell'officer proveniente da Bruxelles

25
Gen

2019
alessandro Sarti
partecipazione a meeting di progetto

nel ciclo di seminari: GHAIA MEETING

presentazione del lavori svolti sul WP5. Il meeting è ristretto ai membri del progetto. Il prof. Sarti è invitato a rimaneree anche al workshop che si svolge il giorno 26 gennaio, e a fare una comunicazione il giorno 28 gennaio

24
Gen

2019
Marco Maggesi
Metodi formali per la pratica matematica

nell'ambito della serie: TOPICS IN MATHEMATICS 2018/2019

La comparsa e la rapida evoluzione dei software di dimostrazione interattiva aprono nuovi scenari nell'impiego, nello sviluppo e nella comunicazione della Matematica. Nella prima parte del seminario si cercherà di fornire un'introduzione generale all'argomento e di dare conto dello stato dell'arte di questa disciplina emergente. Nella seconda parte verrà presentato uno sviluppo dell'analisi quaternionica con il sistema di dimostrazione interattiva HOL Light.

23
Gen

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 2/6

seminario di analisi matematica

See https://phd.unibo.it/matematica/it/didattica/2018-2019

22
Gen

2019
Anton Baranov
The de Branges theory of Hilbert spaces of entire functions and its applications to spectral theory of differential operators 1/6

seminario di analisi matematica

Topics: Growth theory of entire functions. De Branges spaces. Canonical sys- tems and their special cases (Jacobi matrices, Schrödinger operators). Direct spec- tral theory of canonical systems. De Branges version of Phragmén–Lindelöf theorem. Ordering theorem for de Branges spaces. Inverse spectral theory in the regular case. Direct and inverse spectral problems in the singular case.

21
Gen

2019
Federico Corberi
Development of a large fluctuation in a system with a singular distribution probability

seminario di fisica matematica

In this seminar I will first set the stage by discussing the phenomenon, sometimes denoted as "condensation of fluctuations", whereby the probability distribution of certain physical quantities develops non-analytical points in the region of rare events. I will show that this is a quite general feature and I will review some simple statistical mechanical models where it is observed. I will discuss how an explanation of the phenomenon can be given in terms of the duality between large deviation events in the given model and typical events in a new and appropriately biased system. Then, I will turn to consider the problem of studying the evolution leading to a large fluctuation. I will do that by introducing and studying analytically a simple model of many identically and independently distributed microscopic variables evolving by means of a master equation. I will show that the process producing a non-typical fluctuation of a variable N is slow and characterized by the power-law growth of the largest possible observable value of N at a given time. I will discuss the analogy between such dynamical process and the slow kinetics observed in systems brought across a phase-transition.

16
Gen

2019
François Delarue
Mean-Field Games - Lezione III

nel ciclo di seminari: MEAN-FIELD GAMES

seminario di probabilità

16
Gen

2019
Franco Flandoli
Stochastic PDEs - Lezione III

nel ciclo di seminari: STOCHASTIC PDES

seminario di probabilità

16
Gen

2019
François Delarue
Mean-Field Games - Lezione II

nel ciclo di seminari: MEAN-FIELD GAMES

seminario di probabilità

15
Gen

2019
Franco Flandoli
Stochastic PDEs - Lezione II

nel ciclo di seminari: STOCHASTIC PDES

seminario di probabilità

15
Gen

2019
François Delarue
Mean-Field Games - Lezione I

nel ciclo di seminari: MEAN-FIELD GAMES

seminario di probabilità

15
Gen

2019
Franco Flandoli
Stochastic PDEs - Lezione I

nel ciclo di seminari: STOCHASTIC PDES

seminario di probabilità

09
Gen

2019
Pierre Pansu
Differential forms as derivatives of Alexander-Spanier cochains