Archivio 2019

iniziato da 4 minuti

22
Mar

Venerdì
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

 ore 12:00
 presso Seminario II
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

nell'ambito della serie: SEMINARI BAD

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.

08
Feb

2019
Andrea Cosso
TBA

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

seminario di probabilità


06
Feb

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

nell'ambito della serie: SEMINARI BAD

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
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
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
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
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
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