# Archivio 2017

17 Nov 2017
nell'ambito della serie
Complex Analysis Lab
The layer potential approach to the spectra of transmission problems on domains with singularities II
The Neumann-Poincare (NP) operator (or the double layer potential) has classically been used as a tool to solve the Dirichlet and Neumann problems of a domain. However, it also serves as a prominent example in non-self adjoint spectral theory, due to its unexpected behaviour for domains with singularities. Recently, questions from materials science have revived interest in the spectral properties of the NP operator on domains with corners, edges, and conical points. This surge in attention is owed to the connection with resonances of transmission/scattering problems used to model surface plasmons in nanoparticles. I aim to give an overview of recent developments, with particular focus on the NP operator’s action on the energy space of the domain. I will also present recent work for domains in 3D with conical points featuring rotational symmetry. In this situation, we have been able to describe the spectrum both for boundary data in L^2 and for data in the energy space. In the former case, the essential spectrum consists of the union of countably many self-intersecting curves in the plane, and outside of this set the index may be computed as the winding number with respect to the essential spectrum. In the latter case the essential spectrum consists of a real interval. Based on joint work with Johan Helsing and Mihai Putinar.
17 Nov 2017
seminario di algebra e geometria
Solving Mixed Integer Linear Problems with CPLEX/OPL" (Part2)
Roberto Roberti
Optimization Programming Language (OPL) is a powerful, yet intuitive programming language that allows to solve Mixed Integer Linear Problems (MILP) via ILOG CPLEX - one of the most performing general-purpose MILP solvers available on the market. OPL allows to efficiently solve a wide variety of MILP involving thousands of variables and constraints within reasonable computing times. In this series of two seminars, we will show how some classical combinatorial optimization problems (e.g., Traveling Salesman Problem, Generalized Assignment Problem, etc) can be formulated and solved in OPL."
16 Nov 2017
seminario di finanza matematica
Matematica in finanza
Francesco Tam
14 Nov 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
The layer potential approach to the spectra of transmission problems on domains with singularities I
The Neumann-Poincare (NP) operator (or the double layer potential) has classically been used as a tool to solve the Dirichlet and Neumann problems of a domain. However, it also serves as a prominent example in non-self adjoint spectral theory, due to its unexpected behaviour for domains with singularities. Recently, questions from materials science have revived interest in the spectral properties of the NP operator on domains with corners, edges, and conical points. This surge in attention is owed to the connection with resonances of transmission/scattering problems used to model surface plasmons in nanoparticles. I aim to give an overview of recent developments, with particular focus on the NP operator’s action on the energy space of the domain. I will also present recent work for domains in 3D with conical points featuring rotational symmetry. In this situation, we have been able to describe the spectrum both for boundary data in L^2 and for data in the energy space. In the former case, the essential spectrum consists of the union of countably many self-intersecting curves in the plane, and outside of this set the index may be computed as the winding number with respect to the essential spectrum. In the latter case the essential spectrum consists of a real interval. Based on joint work with Johan Helsing and Mihai Putinar
14 Nov 2017
seminario di analisi matematica
nell'ambito della serie
On the regularity of maximal operators
In this talk we will discuss questions about the boundedness and continuity of classical and fractional maximal operators acting on Sobolev spaces and spaces of functions of bounded variation.
14 Nov 2017
seminario interdisciplinare
Solving Mixed Integer Linear Problems with CPLEX/OPL" (Part 1)
Roberto Roberti
Optimization Programming Language (OPL) is a powerful, yet intuitive programming language that allows to solve Mixed Integer Linear Problems (MILP) via ILOG CPLEX - one of the most performing general-purpose MILP solvers available on the market. OPL allows to efficiently solve a wide variety of MILP involving thousands of variables and constraints within reasonable computing times. In this series of two seminars, we will show how some classical combinatorial optimization problems (e.g., Traveling Salesman Problem, Generalized Assignment Problem, etc) can be formulated and solved in OPL."
13 Nov 2017
seminario interdisciplinare
Alan Turing: l'enigma
Giuseppe Rosolini
In occasione della rassegna Scienza al cinema verra' commentato il film "The imitation game" e illustrato il contributo di Turing alla decrittazione di Enigma.
10 Nov 2017
nell'ambito della serie
Complex Analysis Lab
Generalized integration operators on Hardy spaces
Nikolaos Chalmoukis (unibo)
I'll start with presenting some known results about the boundedness and compactness properties of the generalized Cesaro operator, Tg, on Hardy spaces in the unit disc, as well as some of its applications. In the second part we introduce a variant of this operator which depends on an analytic symbol g, and we prove the analogous results for this operator. As an application we generalize a theorem of J. Rattya about complex linear differential equations, and we prove a result about factorization of derivatives of Hardy functions.
09 Nov 2017
seminario di fisica matematica
Infinite-volume mixing for one-dimensional maps with an indifferent fixed point
Marco Lenci
This is joint work with Claudio Bonanno and Paolo Giulietti. We study the properties of ‘infinite-volume mixing’ for two classes of intermittent maps: expanding maps of [0,1] with an indifferent fixed point in 0 preserving an infinite, absolutely continuous measure; and expanding maps of the half-line with an indifferent fixed point at infinity preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. As an application, we use global-local mixing to the prove certain limit theorems for our intermittent maps.
09 Nov 2017
seminario di fisica matematica
Rational "mixing" properties in infinite measure spaces
Jon Aaronson (Tel Aviv University)
I'll start with a review of some "rational" ergodic & mixing properties of infinite measure preserving transformations: HK (Hopf-Krickeberg) mixing, rational weak mixing and rational ergodicity. Then I'll show that some group extensions of "Gibbs-Markov semiflows" are HK mixing. This is done via a local limit theorem for these semiflows.
03 Nov 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Beurling and Lax Theorems on invariant subspaces
Alessandro Monguzzi (Università di Milano)
The study of invariant subspaces of Hilbert space operators is a classical problem in analysis. It is an open question whether every operator on an Hilbert space has an invariant subspace other than the trivial ones, the zero subspace and the whole space. A. Beurling completely characterized the invariant subspaces of the unilateral shift $(a_0,a_1,\ldots)\mapsto(0,a_0,a_1,\ldots)$ on $\ell^2(\mathbb{N})$ modeling the shift operator on $\ell^2(\mathbb{N})$ with the multiplication by $z$ on the Hardy space of the unit disc. Few years later P. Lax proved an analogous result, that is, he characterized the translation invariant subspace of $L^2(0,\infty)$. In this seminar I will illustrate Beurling and Lax's result. Time permitting, I will also present an analogous of Beurling's result in the setting of the quaternionic Hardy space of the unit ball. This result was recently obtained in a joint work with G. Sarfatti.
30 Ott 2017
seminario di algebra e geometria
Il problema di Noether-Lefschtz, estensioni ed applicazioni
Antonella Grassi
Il teorema di Noether-Lefschetz classico afferma che, sotto buone condizioni, una curva liscia in una superficie liscia di grado $d \geq 4$ nello spazio (proiettivo) può essere ottenuta intersecando la superficie con un'altra superficie. Le superfici che non soddisfano queste condizioni formano il "luogo di Noether-Lefschetz". Le proprietà delle componenti di questo luogo sono legate alla geometria delle superfici. Discuterò varie estensioni ed applicazioni.
27 Ott 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
An application of analysis on trees: some trace inqualities for holomorphic functions
Nicola Arcozzi
Why doing analysis on trees, besides the intrinsic interest? We show as application the characterization of the Carleson measures (or "trace measures") for the Dirichlet space. The seminar requires virtually no prerequisite on holomorphic functions.
27 Ott 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Interpolation in Reproducing Kernel Hilbert Spaces I
Nicola Arcozzi
We discuss interpolating sequences for RKHS, with special emphasis on the Dirichlet space. The general plan is to cover in a few hours: - interpolation in RKHS in general; - the case of RKHS with the complete Nevanlinna-Pick property; - the Dirichlet space; -the problem of "onto interpolation" on the Dirichlet space; - the weighted Dirichlet spaces (with the construction of Peter Jones). It would be nice to finish with the recent result of Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter (https://arxiv.org/abs/1701.04885) characterizing the interpolating sequences for the spaces having the complete Nevanlinna-Pick property and their multiplier spaces (volounteers are welcome!).
26 Ott 2017
seminario interdisciplinare
Un sistema di supporto alle decisioni per il fund raising management
Alessandro Pezzi
24 Ott 2017
seminario di algebra e geometria
Nuovi risultati sulle funzioni simmetriche (seminario per il gruppo di ricerca)
23 Ott 2017
seminario di algebra e geometria
Nuovi risultati sulle funzioni simmetriche (seminario per il gruppo di ricerca)
20 Ott 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Equilibrium measures on trees
Matteo Levi
On a metric space (X,d) one can define a set function called capacity which has motivations coming from Physics and which plays a deep role in potential theory and geometric measure theory. It is well known that to any compact subset E of X can be associated a probability measure m on X, called equilibrium measure for E, such that m(E)=cap(E). These measures at present are not well understood. We will present a characterization of equilibrium measures when X is a locally finite tree of infinite depth.
13 Ott 2017
seminario di fisica matematica
Nilpotent orbit of real symmetric pair
Willem De Graaf
Let g = g0 ⊕ g1 be a Z/2Z-graded real semisimple Lie algebra. Then (g, g0) is called a real symmetric pair. An x ∈ g1 is called nilpotent if the adjoint map adx : g → g is nilpotent. We let G0 be a Lie group with Lie algebra g0 acting on g1. The problem is to determine the orbits of G0 on the set of nilpotent elements of g1. We wil show several algorithmic techniques that help with solving this problem. The methods will be illustrated in an example where g is the split real form of the Lie algebra of type D4, and the action of G0 on g1 is isomorphic to the action of SL(2, R) 4 on the tensor product of four copies of R 2 . The nilpotent orbits in this example are of interest in theoretical physics, in particular in the study of black holes. (This is joint work with Heiko Dietrich, Daniele Ruggeri, and Mario Trigiante.)
13 Ott 2017
seminario interdisciplinare
From super Harish-Chandra pairs to Lie supergroups
Fabio Gavarini
I present a new method to associate a Lie supergroup with a super Harish-Chandra pairs (=sHCp's), which provides an equivalence of categories between sHCp's and Lie supergroups. Namely, I provide a (new) functorial construction that, with each (real or complex) super Harish-Chandra pair, associates a (real or complex) Lie supergroup: this functor is then proved to be a quasi-inverse to the natural functor from Lie supergroups (up to details) to super Harish-Chandra pairs, so the two yield equivalences between the corresponding categories. The existence of such equivalences was known (possibly in different contexts, such as the smooth or the complex analytic one), but the construction I present is actually new - I present a different quasi-inverse functor - as it follows a totally different, more geometrical method
13 Ott 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Finitely Generated Ideals in the Nevanlinna Class
Artur Nicolau (Universitat Autònoma de Barcelona)
Interpolating sequences for the Nevanlinna class will be used to discuss a natural problem on finitely generated ideals in the class
13 Ott 2017
seminario interdisciplinare
Homogeneous (para)quaternionic manifolds
D. Alekseevski
13 Ott 2017
seminario di fisica matematica
The Magic Star of Exceptional Periodicity
Piero Truini
I present a periodic infinite chain of finite generalisations of the exceptional structures, including E8, the Exceptional Jordan Algebra (and Pair) and the Octonions.
13 Ott 2017
seminario di analisi numerica
On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
Philippe Toint, The University of Namur, Belgium
This talk discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed whose practical performance is compared to that of other formulations. This comparison is conducted on two data assimilation instances (Burgers equation and the Quasi-Geostrophic model), using two different assumptions on parallel computing environment. Because these variants essentially retain the parallelization advantages of the original proposal, they often --- but not always --- perform best, even for moderate numbers of computing processes.
13 Ott 2017
seminario di fisica matematica
Geometric construction of reduced phase space
Alberto Cattaneo
The reduced phase space of a field theory is the space of its possible initial conditions endowed with a natural symplectic structure. An alternative to Dirac’s method, relying on natural geometric aspects of variational problems, was introduced by Kijowski and Tulczijev. This method also has the advantage of having a natural generalization in the BV context. In this talk, I will explain the method and describe some examples, focusing in particular on the tetradic version of general relativity in four dimensions.
12 Ott 2017
seminario di storia della matematica
Pur con tutti i suoi limiti... Contro una lettura troppo ingenua della matematica in Aristotele
Monica Ugaglia
Aristotele non era un matematico. Si può dire che sia stato un fisico, ma non un fisico matematico. Ciò nonostante non si può dire che non conoscesse la matematica, e che non la usasse. In che modo e con quale competenza è ciò che cercherò di mostrare in questo intervento, prendendo in considerazione in particolare la definizione di infinito potenziale, e le sue conseguenze più immediate.
09 Ott 2017
seminario di fisica matematica
Elastica di Eulero e trave di Timoshenko in grandi deformazioni: problemi di buona posizione e minimi locali dell'energia
Alessandro Della Corte (Sapienza Università di Roma)
Il classico problema delle deformazioni geometricamente non lineari dell’Elastica di Eulero, formulato nel 1744, viene affrontato nel caso di forza esterna distribuita per unità di linea. In particolare, viene mostrata l’esistenza di minimi locali dell’energia e vengono studiate alcune loro proprietà qualitative. Inoltre, si presenta una naturale generalizzazione non lineare del modello di Timoshenko, si studia la buona posizione del relativo problema variazionale e la regolarità delle soluzioni.
09 Ott 2017
seminario di fisica matematica
Somme ergodiche per sistemi dinamici non iperbolici
Stefano Isola (Università di Camerino)
Verranno discussi alcuni risultati sul comportamento asintotico di somme ergodiche per semplici sistemi dinamici non iperbolici, quali le rotazioni irrazionali del cerchio. Per opportune osservabili tali risultati danno informazioni sul tipo di comportamento diffusivo di cammini causali dinamicamente generati. Verrà inoltre mostrato come, per osservabili a variazione limitata e opportuni angoli di rotazione, sia possibile costruire sequenze lacunari lungo le quali le suddette somme ergodiche soddisfano un principio d’invarianza, e ne verrà discussa un’applicazione al biliardo rettangolare periodico.
07 Ott 2017
seminario interdisciplinare
Alan Turing: l'enigma
Giuseppe Rosolini
In occasione della rassegna Scienza al cinema verra' commentato il film "The imitation game" e illustrato il contributo di Turing alla decrittazione di Enigma.
06 Ott 2017
seminario di analisi matematica
Singular differential operators with meromorphic eigenfunctions - part II
P.G. Grinevich
These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.
06 Ott 2017
seminario di analisi matematica
nel ciclo di seminari
Complex Analysis Lab
A crash introduction to Reproducing Kernel Hilbert Spaces.
Nicola Arcozzi
If H is a space of functions defined on some set X, evaluating functions at those points provides additional structure to the space H. If the evaluation functionals are bounded on H, we call the overall structure a Reproducing Kernel Hilbert Space (RKHS). This viewpoint goes back to the early XX century, and it was axiomatized in the early 50's by Bergman and Aronszsajn. In this seminar lecture we want to lay down the basics of the theory as in the seminal article od Aronszajn and provide some examples. In forthcoming seminar, we will explore problems of interpolation in RKHS.
03 Ott 2017
seminario di analisi matematica
Singular differential operators with meromorphic eigenfunctions - part I
P.G. Grinevich
These two talks are based on joint works with S.P. Novikov and R.G. Novikov. Generically the spectral theory of differential operators with singular coefficients is badly defined. But following some ideas of soliton theory we consider a very special subclass of differential operators with meromoprphic coefficients such that: 1. In dimension 1 we assume that all eigenfunctions at all energy levels are meromorphic. 2. In dimension 2 we assume that at one energy level we have sufficiently many locally meromorphic solutions. We show that the spectral theory for such operators can be naturalyy defined, but the Hibert spaces of fucntions should be replaces by pseudo-Hilbert spaces of Potrjagin type. At the first talk we will focus on the 1-dimensinal case. In particular we show, that for such periodic operators the Bloch variety is well-defined. The second part will be dedicated to the 2-dimensional case.
29 Set 2017
seminario di analisi matematica
Integrali singolari con simmetrie aggiuntive
Francesco Di Plinio (University of Virginia)
La trasformata di Hilbert è invariante per traslazioni e dilatazioni della retta reale. La classe degli integrali singolari di Calderón-Zygmund, di cui la trasformata di Hilbert è il paradigma, è chiusa rispetto a tali trasformazioni. In questo seminario ci occuperemo di integrali singolari con invarianze aggiuntive: in particolare dell’operatore di Carleson— invariante per modulazioni— la cui limitatezza implica la convergenza puntuale delle serie di Fourier di funzioni a quadrato integrabile, e delle trasformata di Hilbert lungo campi vettoriali Lipschitz nel piano — invariante per rotazioni — quale modello base di integrali singolari lungo direzioni. Saranno presentati risultati recenti ottenuti in collaborazione con I. Parissis, e separatamente con Guo-Thiele-Zorin, e problemi aperti.
29 Set 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Some problems in potential theory on the polytrees
Pavel Mozolyako
Moving a continuous problem to a discrete setting is a popular and everpresent approach, that (from time to time) allows to single out the geometric and combinatorial issues of the question ad hand. A particular case we are aiming to investigate is the representation of the unit disc (polydisc) by a dyadic tree (cartesian product of dyadic trees), and its connection to Dirichlet type spaces. Following Arcozzi, Rochberg, Sawyer and Wick we give a (very brief) introduction to the potential theory on a polytree, and then present a very incomplete list of related problems.
28 Set 2017
seminario di algebra e geometria
Grassmannian geometry and Fano varieties of K3 type.
Enrico Fatighenti
Seminario riservato al gruppo di ricerca, seconda parte. Subvarieties of Grassmannian (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. In this talk we will give a survey of some recent techniques we developed to study the Hodge theory of this particular class of varieties, and we will present some new examples
26 Set 2017
seminario di algebra e geometria
Grassmannian geometry and Fano varieties of K3 type.
Enrico Fatighenti
Seminario riservato al gruppo di ricerca, prima parte. Subvarieties of Grassmannian (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. In this talk we will give a survey of some recent techniques we developed to study the Hodge theory of this particular class of varieties, and we will present some new examples.
22 Set 2017
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Wolff's proof of Wolff's inequality (in the dyadic setting)
Nicola Arcozzi
In 1983 Tom Wolff proved a surprising inequality which proved to be a pivotal tool in Nonlinear Potential Theory. I will go through Wolff's proof, but in the dyadic setting. Hedberg, L. I.; Wolff, Th. H. Thin sets in nonlinear potential theory. Ann. Inst. Fourier (Grenoble) 33 (1983), no. 4, 161–187.
14 Set 2017
seminario di analisi matematica, interdisciplinare
Network models of spread of brain activity and neurodegeneration
Ashish Raj
In recent years bottom-up network models that aim to capture how various brain processes propagate on the brain’s structural connectivity network have been proposed. These spread models are motivated by mounting evidence that both brain activity and various neurodegenerative diseases spread along fiber pathways and ramify within wider brain circuits in a stereotyped fashion. In the case of functional activity, this gives rise to canonical functional networks. In the case of neurodegeneration, the spread is underpinned by a so-called “trans-neuronal transmission” mechanism shared by all common degenerative pathologies, for example Alzheimer’s disease, Parkinson’s disease, frontotemporal dementia, corticobasal degeneration, etc. In this talk I will describe some of these graph theoretic models of spread. First, I will summarize how conventional graph theory metrics like small-world and path length are used in neuroimaging. Then I will specifically highlight the Network-Diffusion model, which seeks to capture network spread via a diffusive process restricted on the structural connectome. We will review the basic network mathematics that governs these diffusion processes. Finally we will show several examples from neuroimaging studies, specifically addressing how the network diffusion model can capture the relationship between structural connctome and functional connectome. Examples of successful network spread modeling in Alzheimer, Parkinson, frontotemporal dementia and aphasias will be presented.
13 Set 2017
seminario di analisi numerica
Spectral low-rank preconditioners for large linear systems and eigenvalue problems
Luca Bergamaschi
13 Set 2017
seminario di probabilità
nel ciclo di seminari
Seminari di Probabilità
$N$-player games and mean field games with absorption
Luciano Campi
We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It{\^o} equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean field game, the renormalization appears in form of a conditional law. We justify our definition of solution in the usual way, that is, by showing that a solution of the mean field game induces approximate Nash equilibria for the $N$-player games with approximation error tending to zero as $N$ tends to infinity. This convergence is established provided the diffusion coefficient is non-degenerate. The degenerate case is more delicate and gives rise to counter-examples. This talk is based on a joint work with Markus Fischer (Università degli Studi di Padova).
06 Set 2017
seminario di algebra e geometria
Rappresentazioni unitarie di Harish-Chandra
C. Carmeli
Le rappresentazioni di Harish-Chandra di un'algebra di Lie semplice complessa possono essere integrate a ottenere rappresentazioni (infinito dimensionali) dei gruppi di Lie reali semisemplici. In questo talk analizziamo come sia possibile ottenere rappresentazioni unitarie di peso piu' alto fissando un sistema positivo ammissibile.
05 Set 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Iacopo Di Pietro
05 Set 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Fabio Canafoglia
05 Set 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Yanushka Beeharry
05 Set 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Daniele Spinella
28 Lug 2017
seminario di analisi matematica
Spectral theory of the periodic spectral-meromorphic singular operators and the Bloch varieties
Petr Grinevich
We present some recent results obtained in collaboration with S.P. Novikov (Steklov Institute and University of Maryland). We study the spectral theory for ordinary differential operators with special singularities such that all eigenfunctions are locally meromorphic near all real singular points. Such operators are called spectrally-meromorphic. In particular, all singular finite-gap operators satisfy this condition. We show that for periodic spectrally-meromorphic operators the Bloch variety is well-defined, and this observation provides a natural way to show that at least locally our operators can be approximated by the finite-gap ones.
25 Lug 2017
seminario interdisciplinare
Periodic direct problem for the self-focusing Nonlinear Schrodinger equation
Petr Grinevich
We present some recent results obtained in collaboration with P.M. Santini (Universiy of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.
25 Lug 2017
seminario di analisi matematica
Periodic direct problem for the self-focusing Nonlinear Schrodinger equationa
Petr Grinevich
The results presented have been obtained in collaboration with P.M. Santini (University of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.
06 Lug 2017
seminario di analisi matematica
On pseudo H-type Lie algebra (parte II)
Irina Markina
06 Lug 2017
seminario di analisi numerica
Sparse regularization: applications in image processing
Ivan Selesnick
Seminario riservato al gruppo di ricerca di Image Processing di Analisi Numerica
05 Lug 2017
seminario di analisi numerica
Sparse-regularized Least Squares and Nonlinear Smoothing
Ivan Selesnick
In this talk, we describe how certain signal smoothing problems can be formulated using sparse-regularized least squares. The L1 norm is often used for this purpose because it preserves the convexity of the objective function to be minimized. We describe novel non-convex regularizers that outperform the L1 norm, yet preserve the convexity of the objective function.
03 Lug 2017
seminario di algebra e geometria
On the number and boundedness of minimal models of a variety of general type
Diletta Martinelli
Finding minimal models is the first step in the birational classification of smooth projective varieties. After it is established that a minimal model exists some natural questions arise such as: is it the minimal model unique? If not, how many are they? After recalling all the necessary notions of the Minimal Model Program, I will explain that varieties of general type admit a finite number of minimal models. I will talk about a recent joint project with Stefan Schreieder and Luca Tasin where we prove that this number is bounded by a constant depending only on the canonical volume. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family. I will also show that in some cases for threefolds, it is possible to compute this constant explicitly.
03 Lug 2017
seminario di analisi matematica
On pseudo H-type Lie algebras (parte I)
Irina Markina
Abstract: In this mini course we will introduce and study 2-step nilpotent Lie algebras, closely related to the Clifford algeras. The pseudo H-type Lie algebras, are generalisations of the Heisenberg type Lie algebras, introduced by Aroldo Kaplan at 1980 for the study of hypoelliptic operators. The mini course will include the following topics. 1. Definition of pseudo H-type Lie algebras. We give equivalent definitions of the pseudo H-type Lie algebras, that originated from the composition of quadratic forms, the representation of the Clifford algebras and isometric properties of the adjoint operator on the Lie algebra. 2. Relation of pseudo H-type Lie algebras and representations of Clifford algebras. Representations of Clifford algebras can be used for the construction of the Lie algebras if and only if the representation space can be endowed with a non degenerate bi-linear symmetric form, making the representation map skew symmetric with respect to this form. We will explain main difficulties of finding such a non-degenerate bi-linear symmetric form and provide several examples of the construction of the pseudo H-type Lie algebras from the Clifford algebra representations, including those that were introduced by A. Kaplan. 3. We will show the method of construction of a special basis for the pseudo H-type Lie algebras, such that the structural constants of the Lie algebras are always 0, 1 or -1. We show that the Bott periodicity of the Clifford algebras are naturally inherited by the pseudo H-type Lie algebras. It allows to reduce the construction to some basic cases. 4. We will show that infinite number of Clifford algebras leads to the infinite number of pseudo H-type Lie algebras. Moreover, the isomorphism of Clifford algebras is not automatically transmitted to the isomorphism of the Lie algebras. We will provide a complete classification of pseudo H-type Lie algebras. 5. The last topic is the description of automorphism groups of the pseudo H-type Lie algebras. It is not a closed topic still, nevertheless, I will inform on some achieved results.
29 Giu 2017
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
Application of sparse data processing
Ivan Selesnick
28 Giu 2017
Vittorio Loreto
28 Giu 2017
seminario di algebra e geometria
Un teorema di compattezza in omologia persistente invariante per gruppi
Nicola Quercioli
Il confronto metrico è una tematica molto importante nell'ambito dell'analisi topologica dei dati (TDA). Uno strumento per tale confronto è la pseudo-distanza naturale, che misura la differenza fra funzioni a valori reali definite su uno spazio topologico X rispetto a un sottogruppo G del gruppo H di tutti gli omeomorfismi da X in X. Limitazioni inferiori di tale metrica possono essere ottenute calcolando l'omologia persistente delle funzioni considerate. Sfortunatamente tali limitazioni hanno un'invarianza troppo estesa, essendo l'omologia persistente classica invariante rispetto all'azione dell'intero gruppo H. Nel nostro seminario esporremo un nuovo metodo per ridurre tale invarianza a quella ristretta all'azione del solo gruppo G. Questo metodo è basato sull'introduzione, sotto opportune ipotesi, di operatori non espansivi invarianti per G. Nella seconda parte del seminario esporremo un teorema di compattezza per lo spazio topologico di tali operatori, che garantisce la possibilità di ottenere approssimazioni arbitrariamente buone della pseudo-distanza naturale senza ricorrere al suo calcolo diretto, che è notoriamente piuttosto difficile.
27 Giu 2017
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
Sparse Least Squares
Ivan Selesnick
26 Giu 2017
seminario interdisciplinare
La geometria frattale del cervello
Stefano Diciotti e Chiara Marzi (Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi"-Università di Bologna)
Alterazioni morfologiche di varie strutture anatomiche encefaliche sono presenti in numerose malattie neurologiche. La tecnica di imaging in vivo utilizzata come riferimento per la caratterizzazione di tali alterazioni è la risonanza magnetica. La misura delle grandezze morfologiche derivanti dalla geometria Euclidea catturano solo alcuni aspetti parziali della struttura cerebrale e non sono in grado di descriverne la reale complessità, che emerge, ad esempio, da fenomeni multiscala. Uno strumento matematico che si presta alla rappresentazione di strutture complesse e dall'aspetto “rugoso” è la geometria frattale che, attraverso lo studio e l’implementazione numerica dei suoi indici, mette in evidenza una complessità strutturale fisiologica, la quale, nel caso di patologie neurologiche, viene compromessa. Questo seminario è volto a fornire sia una cornice teorica che un’introduzione all'implementazione numerica dei metodi e delle applicazioni della geometria frattale nel campo delle neuro-immagini, con particolare attenzione all'algoritmo di box-counting in 3D. Infine verranno presentati alcuni promettenti risultati di applicazione della dimensione frattale su dataset pubblici ed internazionali.
23 Giu 2017
seminario interdisciplinare
The BV formalism and Quantum gravity (workshop riservato agli esperti del settore)
Andrew Waldron
23 Giu 2017
seminario di fisica matematica
Equivalence of field theories in the BV-BFV formalism: the case of gravity
Michele Schiavina
The BV-BFV formalism is a powerful framework to deal with gauge symmetries in the presence of boundaries. Developed by Cattaneo, Mnev and Reshetikhin, it succeeds in unifying the Lagrangian Batalin-Vilkovisky with the Hamiltonian Batalin-Fradkin-Vilkovisky formalisms, aiming at a functorial realisation of quantisation of gauge theories over manifolds with boundaries, and possibly corners. While doing so, it provides a refinement of the usual notion of equivalence of field theories, showing that what was previously considered equivalent on manifolds without boundaries, might no longer be considered as such. In this talk I will review the basics of the formalism that are necessary to understand the examples of one dimensional gravity with matter and of the four dimensional case of general relativity.
23 Giu 2017
seminario di algebra e geometria
When are two hyperbolic knots equal?
Boštjan Gabrovšek (University of Ljubljana)
We will show that complements of hyperbolic knots can be uniquely triangulated and it is possible to distingush between these knots by combinatorically comparing their triangulations. This fact follows from the following sequence of theorems: the Gordon-Luecke theorem on knot complements, the Mostow rigidity theorem, and the Epstein-Penner-Weeks theorem on the Euclidean decomposition of cusped 3-manifolds. We will also discuss knot symmetry types and show that the unique triangulation also allows us to compute the knot symmetry group.
20 Giu 2017
seminario interdisciplinare
Higher Willmore energy functionals (Mini workshop riservato agli esperti del settore)
Andrew Waldron
We will discuss possible generalizations of the Willmore energy functional
20 Giu 2017
seminario di algebra e geometria
Hyperbolic 3-manifolds
Boštjan Gabrovšek (University of Ljubljana)
In 2003 Perelman proved Thurston's geometrization conjecture, which states that every prime closed 3-manifold can be uniquely split into components, each admitting exactly one of the eight Thurston's geometries. We will show different ways of contructing 3-manifolds (Dehn surgery, glueing poyhedra) and will argue that out of the eight possible geometries, the hyperbolic geometry is the most common one. We will also demonstrate how to visualize hyerbolic manifolds and how to perform computations on them, which we will do in real-time.
19 Giu 2017
seminario di algebra e geometria
Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici
19 Giu 2017
seminario di algebra e geometria
Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici
Sheets, and more in general, the stratifications provided by Jordan classes in a Lie algebra or in an algebraic group have been proven to be related to various problems in representation theory, e.g. representation theory of finite groups of Lie type through character sheaves, the orbit method. In a semisimple Lie algebra, a complete list of semisimple Jordan classes such that the closure of their image through the Steinberg map is normal, is to be found in the works of Richardson, Broer, Douglass-Rohrle. In an ongoing joint work with Giovanna Carnovale, we solve the analogous problem in the case of a semi simple simply connected group.
19 Giu 2017
seminario di algebra e geometria
Quotients for sheets in complex Lie algebras and algebraic groups Quozienti per "sheets" in algebre di LIe e gruppi algebrici
Sheets, and more in general, the stratifications provided by Jordan classes in a Lie algebra or in an algebraic group have been proven to be related to various problems in representation theory, e.g. representation theory of finite groups of Lie type through character sheaves, the orbit method. In a semisimple Lie algebra, a complete list of semisimple Jordan classes such that the closure of their image through the Steinberg map is normal, is to be found in the works of Richardson, Broer, Douglass-Rohrle. In an ongoing joint work with Giovanna Carnovale, we solve the analogous problem in the case of a semi simple simply connected group.
15 Giu 2017
seminario di analisi matematica
Derivate temporali frazionarie ed equazioni di evoluzione
Davide Guidetti
In questo seminario introduciamo le derivate frazionarie di Riemann-Liouville e di Caputo, con alcune delle loro principali proprietà. Concludiamo illustrando alcuni risultati di regolarità massimale per problemi misti al contorno, in cui compaiono tali derivate.
13 Giu 2017
seminario di storia della matematica
A fascinating tool for computations in Early Antiquity: the Anthyphairesis
Prof. Salomon Ofman
In this last lecture “A fascinating tool for computations in Early Antiquity: the Anthyphairesis”, I will present the method called by ancient Greek mathematicians ‘anthyphairesis’ i.e. ‘alternate subtraction’. I will try to understand the origins of this simple but sophisticated algorithm which is the ancestor of what modern mathematicians call ‘continuous fractions’. I will show how it was, or at least could had been used to approximate some fractions in the commensurable case. Finally I will consider whether, as claimed by many modern mathematicians and historians of mathematics, there is any possibility the ‘anthyphairesis’ was a tool at the origins of the discovery of the irrationality.
12 Giu 2017
seminario di algebra e geometria
Verso la persistenza in teoria dei grafi
Lorenzo Zuffi
Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. There are two links between persistent homology and graph theory. The first is represented by the various methods to build simplicial complexes from a weighted graph in order to study those simplicial complexes through persistent homology. The second is the application of the core ideas of persistence theory using invariants from graph theory. For example we studied blocks and edge-blocks along filtrations of a graph, in the way generators are studied in persistent homology.
09 Giu 2017
seminario di analisi numerica
Recent differential advances for monocular 3D shape reconstruction techniques
Roberto Mecca, Universita' di Bologna e University of Cambridge
09 Giu 2017
seminario interdisciplinare
Infinite mixing for maps with an indifferent fixed point
Paolo Giulietti
We study certain one-dimensional maps with indifferent fixed point which possess an infinite invariant measure. It is known that extending the definition of mixing of finite ergodic theory is not trivial, and can lead to various definitions of infinite mixing. We show that our maps are mixing, where the relevant mixing behavior is captured by pairing a global observable and a local observable. Joint work with C. Bonanno and M. Lenci.
08 Giu 2017
seminario di fisica matematica
STRUCTURAL STABILITY IN BIDISPERSIVE CONVECTION MODELS - II
Brian Straughan
We examine a model for thermal convection in a bidispersive porous material. Questions of structural stability are investigated. We show how one obtains continuous dependence on parameters in the problem such as Forchheimer coefficients or the interaction coefficient.
08 Giu 2017
seminario di storia della matematica
The mathematical anti-atomism of Plato’s cosmology II.- Understanding the ‘Khôra’ in the Timaeus
Prof. Salomon Ofman - Université Paris 7
In the second lecture about Plato’s mathematical anti-atomism, “The mathematical anti-atomism of Plato’s cosmology II.- Understanding the ‘Khôra’ in the Timaeus”, I will try to explain the role of the ‘khôra’ (the ‘space’) as a fundamental tool in Plato’s anti-atomism. It is well-known the ‘khôra’ is one of the most puzzling notion in one of Plato’s most difficult dialogues. The modern ‘Zeitgeist’ is that Plato’s cosmology or more exactly cosmogony in the Timaeus, is not so far from some mathematical hallucination without any connection to ‘real’ Physics. I will try to show it is a complete misunderstanding of the text, and in particular the frenetic research of unity in contemporary Physics is the very fundamental objective of Plato’s Timaeus and the ‘khôra’ is an essential tool for such a result.
08 Giu 2017
seminario interdisciplinare
Ergodic and statistical properties of B-free numbers
Francesco Cellarosi
I will present some results about the statistical properties of B-free numbers and the dynamical systems naturally associated to them. These results come from a joint paper with M. Avdeeva and Ya. G. Sinai.
07 Giu 2017
seminario di algebra e geometria
Rappresentazione di gruppi simmetrici in omologia persistente bidimensionale
Nicolas Vercheval
È noto che l'omologia persistente bidimensionale può essere ricondotta all'omologia persistente di una famiglia di funzioni reali. In tale modello si assiste a un fenomeno di monodromia, dato dal fatto che lacci nello spazio dei parametri non inducono, in generale, lacci nello spazio dei punti dei diagrammi di persistenza. Gli elementi di tali diagrammi vengono infatti permutati in maniera funtoriale dall'azione dei cammini chiusi nello spazio dei parametri. In questo seminario mostriamo che per ogni gruppo simmetrico S^n è possibile costruire una funzione filtrante che, tramite il relativo funtore, generi S^n come gruppo di monodromia.
07 Giu 2017
seminario di algebra e geometria
Rappresentazione di gruppi simmetrici in omologia persistente bidimensionale
Nicolas Vercheval
È noto che l'omologia persistente bidimensionale può essere ricondotta all'omologia persistente di una famiglia di funzioni reali. In tale modello si assiste a un fenomeno di monodromia, dato dal fatto che lacci nello spazio dei parametri non inducono, in generale, lacci nello spazio dei punti dei diagrammi di persistenza. Gli elementi di tali diagrammi vengono infatti permutati in maniera funtoriale dall'azione dei cammini chiusi nello spazio dei parametri. In questo seminario mostriamo che per ogni gruppo simmetrico S^n è possibile costruire una funzione filtrante che, tramite il relativo funtore, generi S^n come gruppo di monodromia.
07 Giu 2017
seminario interdisciplinare
Numerical mixing
Roberto Artuso
I will review some theoretical tools which lead to (indirect) numerical schemes to explore rate of mixing for deterministic systems. In particular I will emphasise procedures that involve investigations of Poincar\'e recurrences and the distribution of finite time Lyapunov exponents.
06 Giu 2017
seminario di storia della matematica
The mathematical anti-atomism of Plato’s cosmology I. - An Introduction to the Timaeus
Salomon Ofman - Université Paris 7
. This is first of a two lectures about the ‘Plato’s mathematical anti-atomism’ concerning his cosmology. In the first part, ‘An Introduction to the Timaeus’, I will present an overview of some cosmologies in early Antiquity, beginning with Thales to Democritus, the father of the ‘atomism’. Then I will discuss what we know or can infer about their cosmology through the texts of the most known ancient atomists, Democritus (with Leucippus), Epicurus and Lucretius. According to many scientists and philosophers, among all the doctrines in the Greek and Roman Antiquity, it is the closest to modern scientific thinking. We will consider whether such an assessment is correct or it is a modern representation grounded in an anachronistic reading of the few extant Greek texts on this doctrine.
06 Giu 2017
seminario interdisciplinare
Quantitative mixing for area-preserving flows on compact surfaces
Davide Ravotti
Given a compact surface, we consider the set of area-preserving flows with isolated fixed points. The study of these flows dates back to Novikov in the 80s and since then many properties have been investigated. Starting from an overview of the known results, we show that typical such flows admitting several minimal components are mixing when restricted to each minimal component and we provide an estimate on the decay of correlations for smooth observables.
06 Giu 2017
seminario interdisciplinare
A CLT for cocycles over rotations
Corinna Ulcigrai
We will present an instance of the central limit theorem in entropy zero dynamics obtained as a temporal limit theorem. We consider deterministic random walks on the real line R driven by a rotations (or in other words, a skew product over an irrational rotation) and prove a temporal CLT for badly approximable rotation numbers and piecewise cocycle with jumps at certain irrational values. This generalizes previous results by J.Beck and by D. Dolgopyat and O. Sarig. The proof uses continued fraction and Ostrowsky renormalization. The talk is based on joint work with Michael Bromberg.
05 Giu 2017
seminario di fisica matematica
Structural stability in bidispersive convection models - I
Brian Straughan
We examine a model for thermal convection in a bidispersive porous material. Questions of structural stability are investigated. We show how one obtains continuous dependence on parameters in the problem such as Forchheimer coefficients or the interaction coefficient.
31 Mag 2017
seminario di fisica matematica
Decay and uniqueness in multi-porosity elasticity
Brian Straughan
We discuss models for double and triple porosity elasticity. Uniqueness is proved with no definiteness the elasticities and decay is shown for a quasi-equilibrium model. Open questions are discussed in the full case.
26 Mag 2017
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2016/2017
Modellizzazione di popolazioni di residui dello sparo da inneschi innovativi
Matteo Donghi
26 Mag 2017
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2016/2017
Tentativi di standardizzazione nell'ambito di un approccio quantitativo alle Scienze Forensi: l’approccio statistico nella valutazione dei confronti tra impronte balistiche
Pasquale Iafelice
25 Mag 2017
Stark resonances in a curved wave guide 2
Philippe BRIET (Università di Tolone-Centre de Physique Théorique de Luminy)
We further develop some technical aspects of the results concerning the resonance phenomena in a deformed waveguide.
24 Mag 2017
seminario di algebra e geometria
Pseudo-distanza naturale associata al gruppo di Lie S1 e insieme dei suoi omeomorfismi ottimali.
Alessandro De Gregorio
La pseudo-distanza naturale è una misura di dissomiglianza tra funzioni continue a valori reali definite su uno spazio topologico compatto X, rispetto a un gruppo G di omeomorfismi da X in X. Nel caso che G sia compatto questa pseudo-metrica rappresenta il minimo costo necessario per trasformare una funzione nell'altra tramite la composizione con omeomorfismi appartenenti al gruppo scelto. In questo seminario esaminiamo la pseudo-distanza naturale tra funzioni di Morse definite su S^1 quando G è il gruppo di Lie S^1. Poniamo la nostra attenzione sull'insieme degli omeomorfismi ottimali, cioè quegli omeomorfismi da S^1 a S^1 che trasformano una nell'altra mediante composizione a destra le due funzioni considerate, con un costo di trasformazione misurato dalla norma del sup e pari al valore della pseudo-distanza naturale tra le suddette funzioni. ​
23 Mag 2017
Stark resonances in a curved wave guide 1
Philippe BRIET (Università di Tolone-Centre de Physique Théorique de Luminy)
We analyse the resonance phenomena in a geometrically deformed waveguide. We present résulte about the existence of resonances in these systems. Morover we give some exponential bound with respect to the intensity of the field F, when F is small. These results are obtained in collaboration with Mounira Gharsalli from University El Manar of Tunis.
22 Mag 2017
seminario di analisi matematica
On the quasi-geostrophic equations on compact surfaces in R^3
Jan Prüss
22 Mag 2017
"Introduzione all' Elaborazione del Linguaggio Naturale"
Bernardo Magnini (Fondazione Bruno Kessler - Trento)
Il seminario intende fornire un' introduzione al campo dell' Elaborazione del Linguaggio Naturale (NLP), una delle aree di attività dell’Intelligenza Artificiale. La comprensione automatica del linguaggio, parlato e scritto, continua ad essere una sfida scientifica e tecnologica affascinante e complessa. L’ambiguità a vari livelli (lessicale, sintattico, semantico), l’uso frequente di espressioni non letterali (metaforiche, ironiche, ecc.), la necessità di fare continuo ricorso a conoscenza di background e al contesto extra-linguistico dell’interazione, sono solo alcuni degli aspetti che rendono così difficile simulare le competenze linguistiche delle persone. Il seminario illustra diverse prospettive per rappresentare e trattare oggetti linguistici (parole, frasi, testi) da un punto di vista computazionale: come formule logiche, come eventi aleatori in un sistema probabilistico, come elementi geometrici in spazi multidimensionali. Su queste rappresentazioni si basano le tecniche più diffuse in grado di apprendere da dati, tra cui le reti neurali. Tecnologie che oramai trovano ampio spazio in numerose applicazioni di uso quotidiano, quali i traduttori automatici, la ricerca semantica basata su “knowledge graph”, e gli assistenti personalizzati in grado di rispondere a comandi vocali.
22 Mag 2017
"Introduzione all' Elaborazione del Linguaggio Naturale"
Bernardo Magnini (Fondazione Bruno Kessler - Trento)
Il seminario intende fornire un' introduzione al campo dell' Elaborazione del Linguaggio Naturale (NLP), una delle aree di attività dell’Intelligenza Artificiale. La comprensione automatica del linguaggio, parlato e scritto, continua ad essere una sfida scientifica e tecnologica affascinante e complessa. L’ambiguità a vari livelli (lessicale, sintattico, semantico), l’uso frequente di espressioni non letterali (metaforiche, ironiche, ecc.), la necessità di fare continuo ricorso a conoscenza di background e al contesto extra-linguistico dell’interazione, sono solo alcuni degli aspetti che rendono così difficile simulare le competenze linguistiche delle persone. Il seminario illustra diverse prospettive per rappresentare e trattare oggetti linguistici (parole, frasi, testi) da un punto di vista computazionale: come formule logiche, come eventi aleatori in un sistema probabilistico, come elementi geometrici in spazi multidimensionali. Su queste rappresentazioni si basano le tecniche più diffuse in grado di apprendere da dati, tra cui le reti neurali. Tecnologie che oramai trovano ampio spazio in numerose applicazioni di uso quotidiano, quali i traduttori automatici, la ricerca semantica basata su “knowledge graph”, e gli assistenti personalizzati in grado di rispondere a comandi vocali.
19 Mag 2017
seminario interdisciplinare
nell'ambito della serie
Neuromatematica
Multichannel Harmonic Representation in Early Visual Cortex
Silvio Sabatini
Enabling visually-guided behaviors in artificial agents implies picking-up and organizing appropriate information from the visual signal at multiple levels. The question arises about how to carefully define which feature to extract, or, from a different perspective, which kind of representation to adopt for the visual signal itself. It is well known that receptive fields (RFs) in the early stages of the primary visual cortex behave as band-pass linear filters performing a multichannel representation of the visual signal (cf. the Gabor jets). Typically, visual features are direcly derived, as symbols, from the outputs of such front-end RFs. Here, I want to emphasize the advantages of thinking early visual processes in terms of signal processing, pointing out the key role played by a full harmonic representation of the visual signal and how highly informative properties of the visual signal are efficiently and effectively embedded in the local image phases and their relationships. Accordingly, instead of directly extracting "classic" spatial features (such as edges, corners, etc.) and then looking for correspondences, we can follow a complementary approach: the visual signal is described in frequency bandwidths in terms of local amplitude, phase and orientation, and more complex visual features are derived as "qualities" based on local phase properties e.g., such as phase conguency, phase difference, and phase constancy, for contrast transitions, disparity and motion, respectively. Notably, phase-based interpretation of the visual signal allows direct links between consolidated machine vision computational techniques and the ascertained properties of visual cortical cells. The issue of direct phase-based measurements vs. distributed population coding of visual features will be discussed in relations to motion and stereo perceptual tasks.
19 Mag 2017
seminario di algebra e geometria
Simple reflections, revisited.
Maria Manuel Clementino
We present a notion of simple monad that generalises the notion of simple reflection of Cassidy-Hebert-Kelly to order-enriched categories, and study the factorisations they induce. These factorisations are lax orthogonal and can be characterised by a cancellation property. We will show that filter monads on topological T0-spaces are simple, and show that the factorisations they induced, are lax orthogonal.
18 Mag 2017
seminario di analisi matematica
Fractional Poincaré inequalities on manifolds with finite total Q-curvature
Yannick Sire (Johns Hopkins University)
We establish new fractional Poincaré inequalities encoding geometry of conformally flat manifolds with finite total Q-curvature. The method of proof is based on some improvement of the standard Poincare inequality and harmonic analysis techniques. We will give a description of the underlying geometry and in particular the role of the Q-curvature.
16 Mag 2017
seminario di algebra e geometria
From sets to categories: exponentials and subobject classifiers
Maria Manuel Clementino
IIn this presentation, an introduction of topos theory will be exposed. To this aim it will be shown how the category of sets and functions can be considered an elementary topos.
15 Mag 2017
seminario di algebra e geometria
nell'ambito della serie
Why knot?
Federico William Pasini
The aim of Geometric Group Theory is to get insights on the structure of groups looking at their actions on suitable topological spaces. A significant type of these spaces are classifying spaces for families of subgroups. Classifying spaces for families have been widely studied in the case of the families of finite subgroups and virtually cyclic subgroups, due to their connections with the celebrated Baum-Connes Conjecture and Farrell-Jones Conjecture, respectively. But the definitions are stated for all families of subgroups. The purpose of this seminar is to convince that even off the main road of the two standard families of finite and virtually cyclic subgroups there is fascinating mathematics, that still waits to be explored. In particular, this talk is intended to be an accessible invitation to the investigation of "exotic" classifying spaces in the realm of knot theory. We show how to build a classifying space for a significant family of subgroups of a prime knot group and we investigate its cohomological properties. While playing a little with it, interesting analogies with algebraic number theory will pop out.
15 Mag 2017
seminario di algebra e geometria
nell'ambito della serie
Una, due o nessuna? Unitary representations of free groups and surface groups
Elia Manara
Some years ago M.G.Kuhn and T.Steger introduced a class of unitary representations of free groups which they called multiplicative. This class is large enough to include many examples of unitary representations constructed henceforth. Moreover, multiplicative representations have the very interesting property of being tempered, i.e. weakly contained in the regular representation. After recalling the basic notions needed to enter into the field, we outline some algebraic and analytic properties of these representations and we advance some ideas for extending such a study to surface groups and hyperbolic groups.
11 Mag 2017
seminario di analisi matematica
On the homogeneous Dirichlet problem for the subelliptic eikonal equation
Paolo Albano
abstract: We consider the subelliptic eikonal equation, i.e. the eikonal equation associated with a family of (real) smooth vector fields satisfying the Hoermander bracket generating condition on a neighborhood of an open bounded set with smooth boundary. We study the regularity and the singularities of the viscosity solution of the homogeneous Dirichlet problem for such an equation.
09 Mag 2017
seminario interdisciplinare
nell'ambito della serie
Colloquio di Dipartimento
Matematica, Scienza dei Dati, Scienza dei Sistemi Complessi: la nuova alleanza dell’era digitale
Mario Rasetti
COLLOQUIO DI DIPARTIMENTO C’è una rivoluzione in corso, la rivoluzione digitale: la quantità di dati che produciamo raddoppia ogni anno; nel 2016 abbiamo generato tanti dati quanti ne erano stati prodotti nell’intera storia dell’umanità fino al 2015. Con IoT (Internet of Things) entro 10 anni avremo 150 miliardi di sensori connessi in rete, 20 volte più che il numero di persone sulla Terra. Allora la quantità di dati raddoppierà ogni 12 ore. È la quinta rivoluzione dell’IT: dopo i grandi computer, i pc, internet e il web 1.0, i cellulari e il web 2.0, i Big Data – una rivoluzione dovuta allo tsunami di dati, dove tutto quello che facciamo lascia una traccia digitale. Una rivoluzione paragonabile a quella avvenuta con l’invenzione della stampa. I bits faranno molto più di quanto i caratteri mobili di Gutenberg abbiano fatto in termini di spostamento degli equilibri del potere e di trasferimento della conoscenza dalle mani di pochi a comunità sempre più allargate. L’intelligenza artificiale sta facendo progressi impensati, soprattutto attraverso l’analisi dei dati. L’AI non si programma più riga per riga, ma è ora capace di imparare e di automigliorarsi continuamente: sono ormai standard algoritmi in grado di completare compiti che richiedono ‘intelligenza’ meglio degli uomini. Fra il 2020 e il 2060 i super-computer sorpasseranno le capacità umane in moltissime aree. In questo quadro, da un lato i Big Data dall’altro l’AI impongono compiti di manipolazione dei dati che sono strenui sia per la computer science (nuovi paradigmi computazionali; computazione interattiva; la sfida del 'beyond Turing') che per la 'data analytics' (nuove metodologie di approccio al 'data mining'; analisi dei dati topologica; inferenza causale non lineare) per affrontare problemi complessi, nelle scienze di base (scienze della vita, clima, scienze della terra, …) come in quelle sociali, con la data science (A.I., data mining, machine learning, deep learning, teoria topologica del campo dei dati) e la scienza della complessità (teoria delle reti). Ne segue la necessità di una nuova, forte alleanza che combinando metodi e conoscenze della fisica statistica, della matematica, della computer science permetta alla scienza di affrontare in modo vincente questa sfida epocale. Mario Rasetti è Professore Emerito di Fisica Teorica al Politecnico di Torino ed è Presidente di ISI Foundation, Torino e ISI Global Science Foundation, New York.
09 Mag 2017
seminario di algebra e geometria
Combinatorial Vector Field Dynamics
Tomasz Kaczynski
Forman's discrete Morse theory is an analogy of the classical Morse theory with informal ties numerically explored by computational geometry and visualization communities. In his 1998 paper on "Combinatorial vector fields and dynamical systems", Forman extends his discrete theory to non-gradient combinatorial vector fields with the aim of investigating periodic trajectories. However, his concept of V-paths des not suit analysis of asymptotic dynamics. We extend V-paths so to fill that gap and continue with dynamical attributes such as isolated invariant sets, index pairs, and Morse decomposition. The ultimate goal is to establish a formal tie between continuous and combinatorial vector fields on the level of dynamical systems. This is a joint work with M. Mrozek and Th. Wanner.
08 Mag 2017
seminario di analisi matematica
Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability
Rolando Magnanini
Il Soap Bubble Theorem (SBT) stabilisce che una superficie compatta con curvatura media costante è una sfera. Per dimostrare questo risultato, A. D. Alexandrov ha inventato il suo principio di riflessione, che è stato in seguito perfezionato da J. Serrin nel metodo dei piani mobili, per ottenere la simmetria radiale per una classe di problemi sovra-determinati. H. F. Weinberger ha fornito una dimostrazione del risultato di Serrin basata su alcune identità e disuguaglianze integrali. R. C. Reilly ha infine fatto vedere come il metodo di Weinberger può essere usato per ottenere un'altra dimostrazione del SBT. Nel mio seminario, seguendo le orme di Weinberger e Reilly, farò vedere come i due risultati di simmetria discendano da due identità integrali per la rigidità torsionale di una sbarra. Le due identità saranno poi usate per ottenere risultati di stabilità della configurazione sferica nei due problemi ed in altri problemi analoghi.
08 Mag 2017
seminario di analisi matematica
Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability
Rolando Magnanini
Il Soap Bubble Theorem (SBT) stabilisce che una superficie compatta con curvatura media costante è una sfera. Per dimostrare questo risultato, A. D. Alexandrov ha inventato il suo principio di riflessione, che è stato in seguito perfezionato da J. Serrin nel metodo dei piani mobili, per ottenere la simmetria radiale per una classe di problemi sovra-determinati. H. F. Weinberger ha fornito una dimostrazione del risultato di Serrin basata su alcune identità e disuguaglianze integrali. R. C. Reilly ha infine fatto vedere come il metodo di Weinberger può essere usato per ottenere un'altra dimostrazione del SBT. Nel mio seminario, seguendo le orme di Weinberger e Reilly, farò vedere come i due risultati di simmetria discendano da due identità integrali per la rigidità torsionale di una sbarra. Le due identità saranno poi usate per ottenere risultati di stabilità della configurazione sferica nei due problemi ed in altri problemi analoghi.
04 Mag 2017
seminario di analisi matematica
The Harnack inequality for several classes of sub-elliptic operators.
Erika Battaglia
In this seminar some recent results concerning Harnack inequalities will be presented for several classes of sub-elliptic operators. We will start by considering a class of sub-elliptic operators, in divergence form, with low-regular coefficients under global doubling and Poincaré assumptions; for these operators a non-homogeneous invariant Harnack inequality will be shown. As a consequence, we will prove the solvability of the Dirichlet problem (in a suitable weak sense). In the second part, we will consider a class of hypoelliptic non-Hormander operators for which we have been able to construct a Green function; with a completely different approach with respect to the case of doubling metric spaces, we will conclude by showing (by means of techniques of Potential Theory) how the solvability of the Dirichlet problem has been a fundamental tool in order to prove a homogeneous Harnack inequality in the framework of harmonic spaces.
03 Mag 2017
seminario di finanza matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Alessandro Gianfelici
03 Mag 2017
seminario di finanza matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Francesco Maura
03 Mag 2017
seminario di finanza matematica
Alta Formazione in Finanza Matematica: presentazione didattica e testimonianze
Pier Paolo Chiurchiù
02 Mag 2017
seminario interdisciplinare
Professione Matematico
Monia Tomassini
Sei giovani neo laureati vengono a raccontare agli studenti del corso di laurea e a tutti gli interessati la loro esperienza lavorativa.
02 Mag 2017
seminario interdisciplinare
Professione Matematico
Martina Valeri
Sei giovani neo laureati vengono a raccontare agli studenti del corso di laurea e a tutti gli interessati la loro esperienza lavorativa.
02 Mag 2017
seminario di algebra e geometria
On the topology of the representation variety of a punctured surface group in PSL(2,R)
Gabriele Mondello
Goldman classified the connected components of the representation variety of a closed surface group in PSL(2,R) and Hitchin described the topology of the components with nonzero Euler number. In this talk I will describe how to perform a similar analysis for surfaces with punctures, thus detecting the topology of the representation variety in PSL(2,R) with assigned peripheral monodromy and nonzero Euler number. We follow Hitchin's strategy and we exploit Simpson's correspondence between representations of punctured surface groups and parabolic Higgs bundles.
02 Mag 2017
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
"Applicazione del Metodo degli Elementi Virtuali ad alcuni problemi della Meccanica del Continuo".
Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/
02 Mag 2017
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
"Il Metodo degli Elementi Virtuali per l'approssimazione di problemi di equazioni alle derivate parziali"
Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/
27 Apr 2017
seminario di analisi matematica
Radial positive solutions for p-Laplacian supercritical Neumann problems
Francesca Colasuonno
In this presentation, we will analyze a p-Laplacian problem set in a ball of R^N, with homogeneous Neumann boundary conditions. The equation involves a nonlinearity g which is (p-1)-superlinear at infinity, possibly supercritical in the sense of Sobolev embeddings. The nonlinearity allows the problem to have a constant non-zero solution. In this setting, we prove via shooting method the existence, multiplicity, and oscillatory behavior (around the constant solution) of non-constant, positive, radial solutions. We show that the situation changes drastically depending on p>1. For example, in the prototype case g(s)=s^{q-1}, if p>2, the problem has infinitely many solutions for q>p. While, if p=2, the problem admits at least k non-constant solutions provided that q-2 is bigger than the (k+1)-th radial eigenvalue of the Laplacian with Neumann boundary conditions. Finally, for 1<p<2 a surprising result is found, as non-constant solutions with the same oscillatory behavior appear in couples when the radius of the domain is big enough. We will try to give a unified description and motivation for these three different situations. This is a joint work with Alberto Boscaggin (Università di Torino) and Benedetta Noris (Universitè de Picardie Jules Verne). [A. Boscaggin, F. Colasuonno, B. Noris, Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions, preprint] [F. Colasuonno, B. Noris, A p-Laplacian supercritical Neumann problem, Discrete Contin. Dyn. Syst., Vol. 37 n. 6 (2017) 3025-3057]
27 Apr 2017
seminario di algebra e geometria
Integral closure, mixed multiplicities of ideals and singularity theory 3
Carles Bivià-Ausina (Universitat Politècnica de València)
We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.
27 Apr 2017
seminario di algebra e geometria
Integral closure, mixed multiplicities of ideals and singularity theory 2
Carles Bivià-Ausina (Universitat Politècnica de València)
We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.
26 Apr 2017
seminario di algebra e geometria
Integral closure, mixed multiplicities of ideals and singularity theory 1
Carles Bivià-Ausina (Universitat Politècnica de València)
We review the most important concepts and result regarding the integral closure of ideals and its connection with the multiplicity theory of ideals and modules. We will also see some applications of these notions to the study of singularities of complex analytic maps. In particular, we will recall the celebrated results of Teissier and Gaffney about the equisingularity of analytic deformations of complex maps.
21 Apr 2017
nel ciclo di seminari
Neuromatematica
Emergence of transformation-tolerant representations of visual objects in rat lateral extrastriate cortex
Davide Zoccolan
Rodents are emerging as increasingly popular models of visual functions. Yet, evidence that rodent visual cortex is capable of advanced visual processing, such as object recognition, is limited. In my seminar, I will describe the results of a recent study in which we have investigate how neurons located along the progression of extrastriate areas that, in the rat brain, run laterally to primary visual cortex, encode object information. We found a progressive functional specialization of neural responses along these areas, with: i) a gradual increase of receptive field size and response latency; ii) a sharp reduction of the amount of low-level, energy-related visual information encoded by neuronal firing; and iii) a substantial increase in the ability of single neurons to support discrimination of visual objects under identity-preserving transformations (e.g., position and size changes). These findings strongly argue for the existence of a rat object-processing pathway, and point to the rodents as promising models to dissect the neuronal circuitry underlying transformation-tolerant recognition of visual objects.
20 Apr 2017
seminario di analisi matematica
Flatness results for nonlocal phase transitions in low dimensions.
Eleonora Cinti
We present some recent results in the study of the fractional Allen-Cahn equation. In particular, we are interested in the analogue, for the fractional case, of a well known De Giorgi conjecture about one-dimensional symmetry of bounded monotone solutions. In dimension n=2 and for any fractional power 0<s<1 of the Laplacian, the conjecture is known to be true. In this seminar, we will address the 3-dimensional case. Depending wheter s is below or above 1/2, we need to exploit different techniques and ingredients in the proof of the one-dimensional symmetry. In particular, when s<1/2, some properties of the so-called nonlocal minimal surfaces, will play a crucial role. This talk is based on several papers in collaboration with X. Cabré, J. Serra, and E. Valdinoci.
13 Apr 2017
seminario di analisi matematica
The isoperimetric problem in Carnot-Carathéodory spaces
Valentina Franceschi
The aim of this seminar is to present some results about the isoperimetric problem in Carnot-Carathéodory spaces connected with the Heisenberg geometry. The Heisenberg group is the framework of an open problem about the shape of isoperimetric sets, known as Pansu’s conjecture. We start by studying the isoperimetric problem in Grushin spaces and Heisenberg type groups, under a symmetry assumption that depends on the dimension. We emphasize a relation between the perimeter in these two types of structure. We conclude by presenting some recent results about constant mean curvature surfaces (hence about isoperimetric sets) in the Riemannian Heisenberg group, focusing our attention on the subriemannian limit.
11 Apr 2017
seminario di algebra e geometria
0-cicli su alcune varietà di Calabi-Yau.
Gianluca Pacienza
Nel seminario presentero' un lavoro in collaborazione con G. Bini e R. Laterveer riguardante una congettura di Voisin sugli 0-cicli su varietà con genere geometrico 1. Facendo uso di alcuni risultati di Ch. Vial, ottieniamo un criterio generale da cui dedurre tale congettura per le varietà di Calabi-Yau di dimensione al piu' 5. Presenteremo infine una serie di esempi ai quali è possibile applicare il nostro criterio.
07 Apr 2017
seminario di algebra e geometria
nel ciclo di seminari
Geometria Algebrica e Tensori
Real identifiability and Complex identifiability
Elena Angelini
Abstract. A tensor T of rank k is identifiable when it has a unique decomposition in terms of rank-1 tensors. There are cases in which the identifiability fails over C, for general tensors of fixed rank. The failure, often, is due to the existence of an elliptic normal curve through general points of the corresponding variety of rank-1 tensors. After a brief introduction to the subject, we prove the existence of non-empty euclidean open subsets of some varieties of real k-rank tensors, whose elements have 2 complex decompositions, but are identifiable over R. Moreover we provide examples of non-trivial euclidean open subsets in certain spaces of symmetric tensors and of almost unbalanced tensors, whose elements have real rank equal to the complex rank and are identifiable over R but not over C. On the contrary, there are examples of tensors of given real rank, for which identifiability over R can't hold in non-trivial open subsets. These results have been obtained in collaboration with Cristiano Bocci and Luca Chiantini.
06 Apr 2017
seminario di fisica matematica
Topological dynamics of piecewise lambda-affine maps of the interval
Arnaldo Nogueira
Let $0 < a < 1$, $0 \le c <1$ and $I = [0,1)$. We call contracted rotation the interval map $\phi_{a,c} : x \in I \mapsto ax + c \mod 1$. Once $a$ is fixed, we are interested in the dynamics of the one-parameter family $\phi_{a,c}$, where $c$ runs on the interval $[0,1)$. Any contracted rotation has a rotation number $\rho_{a,c}$ which describes the asymptotic behavior of $\phi_{a,c}$. In the first part of the talk, we analyze the numerical relation between the parameters $a,c$ and $\rho_{a,c}$ and discuss some applications of this map. Then, we introduce a generalization of the contracted rotations. Let $-1 < \lambda < 1$ and $f : [0,1) \to \R$ be a piecewise $\lambda$-affine contraction, that is, there exist points $0 = c_0 <c_1 < ... < c_{n-1} < c_n = 1$ and real numbers $b_1, ..., b_n$ such that $f(x) = \lambda x + b_i$ for every $x \in [c_{i-1}, c_i)$. We prove that, for Lebesgue-almost every $\delta \in \R$, the map $f_{\delta} = f + \delta ({\rm mod} 1)$ is asymptotically periodic. More precisely, $f_{\delta}$ has at most $n + 1$ periodic orbits and the $\omega$-limit set of every $x \in [0,1)$ is a periodic orbit.
06 Apr 2017
seminario di analisi matematica
Characterization of the Palais-Smale sequences for the Conformal Dirac-Einstein equation and applications
Ali Maalaoui - American University of Ras al Khaimah, UAE
In this presentation, we study the behavior of the Palais-Smale sequences of the conformal Dirac-Einstein equation, in 3-dimensional compact Riemannian manifolds. The problem originates from the super-symmetric model of coupling gravity with fermionic energy. Since the energy functional is critical, bubbling occurs. We give here a precise characterization of the violation of the (PS) condition and provide an Aubin type inequality guarantying the existence of solutions. Along the proof we see that this problem is in tight relation with the classical Yamabe problem and the Spinorial version of the Yamabe problem
03 Apr 2017
seminario di algebra e geometria
Rappresentazioni matriciali esplicite dei gruppi simmetrici e delle algebre di Lie generali lineari, 2
Francesco Regonati
30 Mar 2017
seminario di analisi matematica
Local solvability of a class of degenerate second order operators
Serena Federico
In this talk we analyze the local solvability property of a class of degenerate second order partial differential operators with smooth and non-smooth coefficients. The class under consideration exhibits a degeneracy due to the interplay between the singularity associated with the characteristic set of a system of vector fields and the vanishing of a function. In particular we shall show the local solvability property of the class in the neighborhood of a set where the principal symbol of the operator can possibly change sign (which is a property that can negatively affect the local solvability of the operator).
30 Mar 2017
seminario di analisi matematica
Regolarità per minimi di funzionali non uniformemente convessi con coefficienti discontinui
A. Passarelli di Napoli (Univ. "Federico II", Napoli)
Presenterò alcuni risultati di regolarità per minimi vettoriali di funzionali integrali. I funzionali oggetto del nostro studio hanno densità di energia f(x,Du) che, rispetto alla variabile gradiente, sono uniformemente convesse e con struttura radiale solo all'infinito. Assumeremo che f abbia crescita p-q, con 2\le p\le q e che la dipendenza dalla x sia controllata attraverso una funzione appartenente allo spazio di Sobolev W^{1,n} e proveremo la maggiore differenziabilità e la maggiore integrabilità locale del gradiente dei minimi. Inoltre, faremo vedere che, nel caso in cui le densità di energia soddisfino condizioni di crescita standard, cioè p=q, il gradiente dei minimi appartiene localmente a L^s, per ogni s>1. Bibliografia: G. Cupini, F. Giannetti, R. Giova, A. Passarelli di Napoli. Higher integrability estimates for minimizers of asymptotically convex integrals with discontinuous coefficients. Nonlinear Anal. 154 (2017), 7-24. G. Cupini, F. Giannetti, R. Giova, A. Passarelli di Napoli. Higher differentiability for minimizers of integrals with non standard growth conditions and discontinuous coefficients. Preprint 2017.
30 Mar 2017
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2016/2017
Curve ellittiche, K3 e l'importanza di essere simplettico
Mongardi
Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.
29 Mar 2017
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
"Applicazione del Metodo degli Elementi Virtuali ad alcuni problemi della Meccanica del Continuo".
Carlo Lovadina , Dipartimento di Matematica, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano , Email: carlo.lovadina@unimi.it , Web: http://www.mat.unimi.it/users/lovadina/
29 Mar 2017
nell'ambito della serie
Topics in Mathematics 2016/2017
"Il Metodo degli Elementi Virtuali per l'approssimazione di problemi di equazioni alle derivate parziali"
> Carlo Lovadina > Dipartimento di Matematica, Università degli Studi di Milano > Via Cesare Saldini 50, 20133 Milano > Email: carlo.lovadina@unimi.it > Web: http://www.mat.unimi.it/users/lovadina/
28 Mar 2017
seminario di analisi matematica
nell'ambito della serie
Topics in Mathematics 2016/2017
Curve ellittiche, K3 e l'importanza di essere simplettico
Mongardi
Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.
27 Mar 2017
seminario di algebra e geometria
Rappresentazioni matriciali esplicite dei gruppi simmetrici e delle algebre di Lie generali lineari, 1
Francesco Regonati
Si descriverà un approccio diretto alla rappresentazione di Gelfand-Tsetlin delle algebre di Lie generali lineari: per ogni gl(n)-modulo semplice si costruirà una base e si ricaverà una formula per la rappresentazione dei generatori di Chevalley di gl(n) rispetto ad essa. Per ottenere le basi si costruiranno esplicitamente i morfismi di branching; per ricavare la formula si fattorizzeranno i morfismi di branching come composizione di certi morfismi elementari e si dimostrerà una identità fra le composizioni di due morfismi elementari. Per specializzazione, si otterrà la rappresentazione seminormale di Young dei gruppi simmetrici: per ogni S_n-modulo semplice si otterrà una base ed una formula per la rappresentazione dei generatori di Coxeter di S_n rispetto ad essa. Gli elementi dei moduli verranno descritti tramite bitableau, i morfismi di branching e i morfismi elementari tramite bitableau di Capelli; le relazioni riguardanti bitableau e bitableau di Capelli saranno provate in un ambito virtuale superalgebrico.
23 Mar 2017
seminario di fisica matematica
Lo schema di rottura minimale della simmetria di replica nei sistemi complessi
Francesco Guerra, Dipartimento di Fisica, Universita' di Roma "La Sapienza" Istituto Nazionale di Fisica Nucleare, Sezione di Roma
Passeremo in rassegna i concetti di simmetria di replica e di rottura spontanea della simmetria di replica per i sistemi complessi, in un contesto semplice ed elementare, ma matematicamente rigoroso. La terminologia consueta, storicamente motivata, ha un valore simbolico altamente suggestivo, anche se alquanto impreciso. Vedremo che la cosiddetta rottura della simmetria di replica ha profonde origini di tipo termodinamico. Investigheremo il caso in cui la simmetria di replica e' rotta in maniera minimale. In alcuni modelli questo schema conduce alla soluzione esatta, come per esempio per il REM (random energy model). In generale, si ottengono comunque delle informazioni sull'energia libera, senza la necessita' di postulare un particolare schema di rottura.
23 Mar 2017
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2016/2017
Curve ellittiche, K3 e l'importanza di essere simplettico
Mongardi
Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.
21 Mar 2017
seminario interdisciplinare
The Minsky Moment and the Revenge of Entropy
J. Barkley Rosser, Jr. - James Madison University
Considering macroeconomies as systems subject to stochastic forms of entropic equilibria, we shall consider how deviations driven by positive feedbacks as in a speculative bubble can drive such an economy into an anti-entropic state that can suddenly collapse back into an entropic state, with such a collapse taking the form of a Minsky moment. This can manifest itself as shifts in the boundary between the portion of the income distribution that is best modeled as Boltzmann-Gibbs and that best modeled as a Paretian power law.
21 Mar 2017
nell'ambito della serie
Topics in Mathematics 2016/2017
Curve ellittiche, K3 e l'importanza di essere simplettico
Mongardi
Partendo dall'esempio delle curve ellittiche, darò una breve introduzione ad alcune varietà complesse Ricci piatte. Nel caso delle superfici, queste sono esclusivamente dei tori complessi o delle superfici semplicemente connesse dette K3. Dopo aver analizzato le loro proprietà in bassa dimensione, passeremo ai casi di dimensione più alta, guardando analogie e differenze.
17 Mar 2017
seminario interdisciplinare
nell'ambito della serie
Neuromatematica
Morphology revision - from an experimental viewpoint.
Liliana Albertazzi
16 Mar 2017
seminario di analisi matematica
KP theory, total positivity and rational degenerations of M-curves
Simonetta Abenda
It is well known that real regular bounded KP (n-k,k)-line solitons are associated to soliton data in the totally non-negative part of the Grassmannian Gr(k,n) and that, in principle, they may be obtained in a certain limit from regular real quasi--periodic KP solutions. The latter class of KP solutions correspond to algebraic geometric data a la Krichever on regular M-curves according to a theorem by Dubrovin-Natanzon. In this talk I shall present some new results recently obtained in collaboration with P.G. Grinevich (LITP-RAS and Moscow State University). The purpose of our research is the connection of such two areas of mathematics using the real finite gap theory of the KP equation. I shall explain how we associate to any KP soliton data in the real totally nonnegative part of Gr(k,n) the rational degeneration of an M-curve of genus g=k(n-k) and the effective KP divisor.
16 Mar 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
“Mini-workshop on mathematical finance”
Francesco Paglione, Daniele Monzali, Alessandro Bonafede, Andrea Pellegrini
Necessaria iscrizione a finanza@dm.unibo.it
14 Mar 2017
seminario di finanza matematica
Systemic risk due to common exposures: stochastic models, dynamical systems, and statistical inference
Fabrizio Lillo
13 Mar 2017
seminario di algebra e geometria
nell'ambito della serie
Seminario di Algebra
Linearità di mapping class group, 2
Alessia Cattabriga
10 Mar 2017
seminario di analisi matematica
Hilbert Module approach to operator theory II
Jaydeb Sarkar
The second talk will be about: Drury-Arveson space, free resolutions, rigidity, Ando dilation, new approach to 2 variables von-Neumann inequality, simple submodules and quotient modules over polydisc.
10 Mar 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Il rischio di controparte in ambito bancario e nel risparmio gestito. Un approfondimento sul Bail in.
Sara Zaltron
09 Mar 2017
seminario di analisi numerica
Sparse X-ray tomography for medical imaging
Samuli Siltanen (University of Helsinki)
X-ray tomography is based on recording several radiographs of a target along different projection directions. The inner structure of the target is then recovered from the data, interpreted as a collection of line integrals over a non-negative X-ray attenuation function. In recent years, mathematical methods have enabled three-dimensional medical X-ray imaging using much lower radiation dose than before. The idea is to collect fewer projection images than traditional computerized tomography machines and then use advanced inversion mathematics to reconstruct the tissue from such incomplete data. One particularly successful methodology is to regularize the inversion by enforcing sparsity in some suitable basis. In this talk we discuss the traditional total variation regularization, leading to sparsity in the image gradient, and sparsity in the shearlet basis. Computational results are shown, based on both simulated and measured data. Also, discussed is a commercial dental low-dose X-ray imaging product based on sparsity-promoting inversion. Special attention is given to automatic choice of regularization parameters.
08 Mar 2017
seminario interdisciplinare
Metodi quantitativi per la gestione del Fund Raising
Alessandro Pezzi
07 Mar 2017
seminario di analisi matematica
Hilbert Module approach to operator theory I
Jaydeb Sarkar
We will begin by briefly describing some of the reasons to be interested in Hilbert module approach to operator theory. Then we will review some recent results and developments in function theory and (multivariable) operator theory. Along the way, we will discuss a list of examples and (wild) conjectures. The first talk will focus on: classical Sz.-Nagy and Foias dilation theory, von Neumann inequality, Beurling-Lax-Halmos theorem, submodules, quotient modules along with a quick introduction of reproducing kernel Hilbert spaces.
07 Mar 2017
seminario di algebra e geometria
nell'ambito della serie
Seminario di Algebra
Hodge theory, graded rings and Grassmannians
Enrico Fatighenti
One of the most classical results in Hodge theory is Griffiths' description of the Hodge filtration of a smooth projective hypersurface in terms of a very explicit polynomial algebra, the so-called Jacobian ring. This turns to be extremely useful in solving Torelli-type problems, amongst others. Griffiths' result has been generalised to the smooth projective complete intersection case by Dimca et al., but not much other progress has been made so far. In this talk we present two different generalisations of Griffiths' theory. First we show how to attach to a smooth projective variety (with no hypotheses on the codimension) a graded module that controls (part of) its Hodge theory and deformation theory (joint work with Carmelo Di Natale/Domenico Fiorenza). Then we analyze the case of smooth hypersurfaces in Grassmannians, and show how to construct an explicit analogue of the Jacobian ring in this case.
07 Mar 2017
seminario di algebra e geometria
nel ciclo di seminari
Kantor Triple Systems
Kantor triple systems and supergravity
Andrea Santi
Verran no illustrate le applicazioni dei Kantor triple systems alla supergravita
06 Mar 2017
seminario di algebra e geometria
nell'ambito della serie
Seminario di Algebra
Linearità di Mapping Class Group, 1
Alessia Cattabriga
Dopo aver introdotto e descritto le principali caratteristiche del mapping class group di una superficie, si indagherà il problema dell'esistenza di rappresentazioni lineari fedeli per tali gruppi. Si presenteranno i risultati noti in quest'ambito, con particolare riguardo alla dimostrazione di linearità per i mapping class group del disco puntato (i.e. i gruppi treccia) e si discuteranno le possibili tecniche per affrontare i casi aperti.
06 Mar 2017
seminario di algebra e geometria
nel ciclo di seminari
Kantor Triple Systems
Andrea Santi
Verranno descritte le Z-graduazioni di profondita 5 delle algebre di Lie semplici (su C)
02 Mar 2017
seminario di analisi matematica
An Inverse Problem in Potential Theory for Picone Elliptic-Parabolic PDEs.
Ermanno Lanconelli (Alma Mater Studiorum Università di Bologna)
Let $\Omega$ be a domain in ${\mathbb{R}^N$. A density with the mean value property for non-negative harmonic functions in $\Omega$ is a positive l.s.c. function $w$ such that, for a suitable $x_0 \in \Omega$, $$u(x0) = \frac{1}{w(Ω)} \nt_{\Omega} u(y)w(y)dy$$ for every non-negative harmonic function $u$ in $\Omega$. In this case we say that $(\Omega,w,x_0)$ is a $\Delta$-triple. Existence of $\Delta$-triples on every suﬃcently smooth domain has been proved in 1994-1995, by Hansen and Netuka, and by Aikawa. Very recently, we have given positive answers to the following inverse problem: “Let $(\Omega,w,x_0)$ and $(D,w',x_0)$ be $\Delta$-triples such that $\frac{w }{w(\Omega)= \frac {w'}{w'(D)} in$D ∩Ω$. Then is it true that$ \Omega = D$?” Our result contains, as particular cases, several classical potential theoretical characterizations of the Euclidean balls. Densities with the mean value property for solutions to wide classes of Picone’s elliptic-parabolic PDEs have appeared in literature since the 1954 pioneering work by B.Pini on the mean value property for caloric functions. In this talk we present an abstract inverse problem Theorem allowing to extend the previously recalled result on the$ \Delta\$-triples to elliptic, parabolic and sub-elliptic PDEs. The results have been obtained in collaboration with Giovanni Cupini (Universita' di Bologna).
01 Mar 2017
seminario di probabilità
nel ciclo di seminari
Seminari di Finanza Matematica
Information, arbitrage, and the price of informational arbitrage
Claudio Fontana
In financial markets, the introduction of inside information can lead to profitable trading opportunities and, in particular, to arbitrage possibilities. In the context of stochastic finance, this issue can be addressed by relying on the theory of enlargement of filtrations. We present some simple examples where informational arbitrage is possible and study the absence of arbitrage under additional information in the context of general semimartingale models. Finally, we try to determine the value of a private information which allows to realize arbitrage opportunities.
28 Feb 2017
seminario di storia della matematica
Definizione degli enti matematici in Aristotele
Monica Ugaglia, Universita' di Firenze
Esempi significativi delle definizioni aristoteliche degli enti matematici principali.
28 Feb 2017
seminario di algebra e geometria
STABILITÀ DI MISURE SU VARIETÀ DI KÄHLER
Alessandro Ghigi (Universita' di Pavia)
Presenterò una versione dell'applicazione momento valida per azioni di gruppi riduttivi su spazi topologici piuttosto generali. Mostrerò che i criteri numerici per la stabilità valgono in questa generalità. Infine considererò una azione di un gruppo riduttivo su una varietà kähleriana e mostrerò che la versione dell'applicazione momento appena descritta si applica all'azione indotta sulle misure sulla varietà. In questo modo si ottiene un criterio per la stabilità di un misura rispetto a questa azione. (Lavoro in collaborazione con Leonardo Biliotti.)
28 Feb 2017
seminario di storia della matematica
Presentazione del libro: "Euclide: Il I libro degli elementi. Una nuova lettura"
Lucio Russo, Università di Roma Tor Vergata
Si presenta la traduzione commentata del Libro I degli Elementi di Euclide, eseguita in collaborazione Giuseppina Pirro , docente di Greco, e Emanuela Salciccia, decente di Matematica e Fisica, nel Liceo Classico Tasso di Roma
28 Feb 2017
seminario di algebra e geometria
Sottovarieta' di Shimura contenute nel luogo di Torelli e nel luogo di Prym.
Paola Frediani (Universita' di Pavia)
Parlero' di alcuni risultati sulle sottovarieta' totalmente geodetiche di A_g contenute nel luogo di Torelli mediante lo studio della seconda forma fondamentale della mappa di Torelli. Spieghero' inoltre la costruzione di esempi di sottovarieta' di Shimura contenute nel luogo di Torelli e nel luogo di Prym per generi bassi ottenuti tramite famiglie di rivestimenti du Galois della retta proiettiva. Si tratta di risultati ottenuti in collaborazione con Elisabetta Colombo, Alessandro Ghigi e Matteo Penegini.
28 Feb 2017
seminario interdisciplinare
Symmetry of asymmetric quantum Rabi models
Masato WAKAYAMA
The (symmetric) quantum Rabi model appears ubiquitously in various quantum systems and its applications include quantum information technology. In this talk, using the representation theory of the Lie algebra sl2, we present a picture of the asymmetric quantum Rabi model equivalent to the one drawn by confluent Heun ordinary differential equations. We show the existence of spectral degeneracies (level crossings in the spectral graph) of the asymmetric quantum Rabi model when the symmetry-breaking parameter equals 1/2 by studying the constraint polynomials, and give a conjectural formula that ensures the presence of level crossings for general half-integers. This result on level crossings was demonstrated numerically by physicists Li and Batchelor in 2015, investigating an earlier empirical observation by Braak (2011). In the picture, we find also a certain reciprocity described by sl2.
24 Feb 2017
seminario di probabilità
nel ciclo di seminari
Seminari di Finanza Matematica
Analytical approximations of non-linear SDEs of McKean-Vlasov type
Stefano Pagliarani
We provide analytical approximations for the law of the solutions to a certain class of scalar McKean-Vlasov stochastic differential equations (MKV-SDEs) with random initial datum. "Propagation of chaos" results (Sznitman 1991) connect this class of SDEs with the macroscopic limiting behavior of a particle, evolving within a mean-field interaction particle system, as the total number of particles tends to infinity. Here we assume the mean-field interaction only acting on the drift of each particle, this giving rise to a MKV-SDE where the drift coefficient depends on the law of the unknown solution. By perturbing the non-linear forward Kolmogorov equation associated to the MKV-SDE, we perform a two-steps approximating procedure that decouples the McKean-Vlasov interaction from the standard dependence on the state-variables. The first step yields an expansion for the marginal distribution at a given time, whereas the second yields an expansion for the transition density. Both the approximating series turn out to be asymptotically convergent in the limit of short times and small noise, the convergence order for the latter expansion being higher than for the former. The resulting approximation formulas are expressed in semi-closed form and can be then regarded as a viable alternative to the numerical simulation of the large-particle system, which can be computationally very expensive. Moreover, these results pave the way for further extensions of this approach to more general dynamics and to high-dimensional settings.
23 Feb 2017
seminario di analisi matematica
Direct and Inverse Problems for Degenerate Differential Equations
Angelo Favini
We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on (−∞;∞). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too. Keywords: Inverse problem; First-Order problem, Second-Order problem, c0−semigroup, Periodic Solution. Joint work with: Mohammed AL Horani; Mauro Fabrizio; Hiroki Tanabe
17 Feb 2017
seminario di analisi numerica
nell'ambito della serie
Neuromatematica
Can one hear the shape of a neuronal network?
Giovanni Naldi
Along the last years the technological advancements have been fundamental to improve the recording capability from brain areas and neural populations. For example multi-site recordings can be achieved from thousands of channels (sites) with a good spatial and temporal resolution yielding a good description of the underlying network dynamics. Given that, the brain operates on a single trial basis such recordings are becoming important to understand the neural code. As a first step, multi-site recordings allow to quantify the information flow in the network. The anatomical wiring (i.e. Structural Connectivity, SC) clearly plays a fundamental role to understand how cells communicate among them but it is often not well known neither it can by itself explain the overall network activity. Multi-site recordings can be used to infer statistical dependencies (i.e. Functional Connections, FC) among the recorded units and to track the information flow in the network. On the other hand the Effective Connectivity (EC) denotes the directed causal relationship between the recorded sites. Experimentally, the EC is typically estimated by stimulating one cell and studying the effects on the connected elements. Alternatively the EC can also be studied by using a causal mathematical model between the recorded units data. Importantly, multi-site recordings raise some limitations that need to be evaluated carefully before any further analysis. First, the experimental sessions are often limited in time. Second, the high dimensional data sets involve a set of numerical and mathematical problems that would be hard to face even with long enough recording sessions. These issues are common to different fields and have been coined as “curse of dimensionality”. In order to capture nonlinear interactions between even short and noisy time series, we consider an event- based model. Then, we involve the physiological basis of the signal, which is likely to be mainly nonlinear. Specifically, we suppose that we are able to observe the dynamical behaviours of individual components of a neuronal networks and that few of the components may be causally influencing each other. The variables could be time series from different parts of the brain. In order to introduce our method we have considered a simulated cerebellar granule cell network capturing nonlinear interactions between even short and noisy time series. Although the proposed EC algorithm cannot be applied straightforwardly to the experimental data, our preliminary results are quite promising. This is a joint work with G. Aletti, T. Nieus, and M. Moroni.
16 Feb 2017
seminario di probabilità
nel ciclo di seminari
Seminari di Finanza Matematica
Randomization method in stochastic optimal control
Andrea Cosso
The talk is about a recently introduced methodology in stochastic optimal control theory, known as randomization method, firstly developed for classical Markovian control problem in the paper: I. Kharroubi and H. Pham "Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE", Ann. Probab., 2015. The randomization method consists, in a first step, in replacing the control by an exogenous process independent of the driving noise and in formulating an auxiliary (“randomized”) control problem where optimization is performed over changes of equivalent probability measures affecting the characteristics of the exogenous process. We will discuss the main features of this approach, showing that the randomization method allows for greater generality beyond the Markovian case. In particular, we may consider stochastic control problems with path-dependence in the coefficients (with respect to both state and control), without requiring any non-degeneracy condition on the controlled equation. The talk is based on joint works with E. Bandini, M. Fuhrman, H. Pham.
16 Feb 2017
seminario di analisi matematica
Characterizing spheres in C^2 by their Levi curvature: a result à la Jellett
Giulio Tralli
In this talk we discuss a rigidity result for a class of real hypersurfaces in C^2 with constant Levi curvature. Following old techniques due to Jellett, we consider the boundaries of starshaped domains which satisfy a suitable condition. We provide as application an Aleksandrov-type result for domains with circular symmetries. This is a joint work with V. Martino.
15 Feb 2017
seminario interdisciplinare
Federigo Enriques scienziato e umanista
Ciro Ciliberto
13 Feb 2017
seminario di analisi matematica
Scattering on the point scatterers.
Petr G. Grinevich
The point scatterers were introduced in middle of 1930-ies as a simple model of nuclear interactions by Bethe, Peierls and Fermi. The strict functional-analytic interpretation was suggested by Berezin and Faddeeev. One of the principal problems of the multidimensional scattering theory is the lack of exactly solvable systems. We calculate the Faddeev (complex momenta) eigenfunctions for a system of point scatterers and show that this model is useful to check some hypotheses about the behavior of the Faddeev eigenfunctions in the complex domain.
09 Feb 2017
seminario di analisi matematica
Un risultato di stabilità asintotica per il flusso non locale di Mullins-Sekerka e per quello di Hele-Shaw
Nicola Fusco (Università di Napoli, Federico II)
Nel seminario presenteremo un risultato di minimalità locale per un’energia ottenuta come limite del modello di Ohta-Kawasaki. Utilizzando tale risultato mostreremo che le configurazioni tridimensionali periodiche, strettamente stabili per il funzionale dell’area, sono esponenzialmente stabili sia per il flusso non locale di Mullins-Sekerka che per quello di Hele-Shaw.
08 Feb 2017
seminario di analisi matematica
Moutard transformations and generalized analytic functions with special contour singularities
Petr G. Grinevich
In 1988 P.G. Grinevich and S.P. Novikov showed that in the fixed-energy scattering problem for the two-dimensional Schrodinger operator one has to study Vekua-Bers generalized analytic functions with special contour singularities. For sufficiently long period no approaches for studying such problems were known. Recently we understood that the Moutard transformation can be applied to the study of generalized analytic functions with such special singularities
07 Feb 2017
seminario di algebra e geometria
nel ciclo di seminari
Kantor Triple Systems
Kantor Triple Systems
Andrea Santi
Verranno discussi i collegamenti tra i Kantor Triple Systems e le algebre di Lie. In particolare verra` proposta una generalizzazione della costruzione di Tits Kantor Koecher. Sono programmati tre incontri da un'ora ciascuno nei giorni 7 febbraio, 14 febbraio, 28 febbraio alle ore 14:30.
31 Gen 2017
seminario di algebra e geometria
nell'ambito della serie
Seminario di Algebra
Una famiglia numerabile di varietà log Calabi-Yau
Gilberto Bini
Enunciata negli anni '50 del secolo scorso per una varietà compatta di Kaehler, la congettura di Calabi è stata dimostrata circa venti anni dopo da Shing-Tung Yau, il quale ha costruito metriche di Kaehler Ricci piatte su varietà compatte con fibrato canonico banale. Tali varietà prendono il nome di varietà di Calabi-Yau e in dimensione complessa uno o due sono tutte diffeomorfe. Al contrario, in dimensione tre non è nemmeno noto se il valore assoluto della loro caratteristica di Eulero è limitato. Se una soluzione a questo problema sembra ancora molto difficile, ha senso porsi la stessa domanda per le varietà log Calabi-Yau. Una volta ricordata la loro definizione nel corso del seminario, mostreremo una costruzione, realizzata in collaborazione con il dott. Filippo F. Favale, di una famiglia numerabile di varietà log Calabi-Yau, per cui l'insieme delle rispettive caratteristiche di Eulero è illimitato inferiormente.
30 Gen 2017
seminario di analisi matematica
Stabiità condizionale per un'equazione parabolica retrograda a coefficienti non lipschitziani
Daniele Del Santo
26 Gen 2017
seminario di analisi matematica
Sparse domination of singular integral operators.
Francesco di Plinio
Singular integral operators, which are a priori signed and non-local, can be dominated in norm, pointwise, or dually, by sparse averaging operators, which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather immediate estimates for the averaging operators. In this talk, we present several positive sparse domination results of singular integrals falling beyond the scope of classical Calderón-Zygmund theory; notably, modulation invariant multilinear singular integrals including the bilinear Hilbert transforms, variation norm Carleson operators, matrix-valued kernels, rough homogeneous singular integrals and critical Bochner-Riesz means. Joint work with Amalia Culiuc and Yumeng Ou and partly with Jose Manuel Conde-Alonso, Yen Do and Gennady Uraltsev.
26 Gen 2017
seminario di algebra e geometria
Persistence is (not) Morse Theory
Ulrich Bauer, Technische Universität München
I will survey the relationship between Morse theory and persistent homology from different aspects: historical connections, discrete Morse theory of geometric filtrations, simplification by Morse cancelation of persistence pairs, algebraic Morse theory, and persistence computation. I will illustrate how the conceptual differences between persistence and Morse theory provide complementary viewpoints, and how an understanding of their interplay can lead to drastic improvements in computational methods.
23 Gen 2017
seminario di algebra e geometria
nel ciclo di seminari
Seminari di Algebra
La corrispondenza di Springer - Parte quinta
Luca Migliorini
Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso.
20 Gen 2017
seminario di finanza matematica
nell'ambito della serie
Finanza Matematica
Extreme Value Theory and Applications
Alessio Brussino
19 Gen 2017
seminario di didattica della matematica
Esempi e controesempi: un punto di vista cognitivo e didattico
Samuele Antonini
18 Gen 2017
seminario interdisciplinare
Word embedding: Deep Learning and Computational Topology for the evaluation of context-based semantic change
Mattia G. Bergomi
Recently, artificial intelligence and deep learning started to occupy a central role in applications. Despite their effectiveness, it is often hard to interpret the inner representation of data provided by these systems. We will present one of the most popular architectures to generate word embeddings: A geometric representation of words dependent on the context in which they can be found in a given dataset. Thereafter, we will take advantage of this model to analyse the semantic shift of words, when used in two different contexts. In particular, we will show how the t-distributed stochastic neighbours embedding can provide a reasonable low-dimensional representation of word embeddings, allowing to explore their most "persistent" regions, through topological methods. Keywords: Artificial intelligence, lyrics, word embedding, semantic shift 75 minutes talk, 45 minutes discussion.
17 Gen 2017
seminario interdisciplinare
Time series topology, a quest towards optimal granularity: automatic stylistic classification
Mattia G. Bergomi
Music can be interpreted as a collection of meaningful events distributed in time. The construction introduced during the first seminar neglects this time-dependent interpretation. Temporal evolution allows the composer to introduce a musical idea, then shape it, and finally proceed to a new scenario. Would it be possible to refine our analysis by representing music in a variable geometry space? We will present a primal attempt to describe this time-dependency in topological terms. First, we will suggest an adaptation of the persistent homology formalism to the analysis and classification of time series. Second, we will analyse different dataset in order to understand the role played by the granularity at which we describe musical events, with respect to our perception. Keywords: Time series, persistent homology, vineyards, Dynamic Time Warping 75 minutes talk, 45 minutes discussion.
16 Gen 2017
seminario interdisciplinare
Persistent homology as a musical fingerprint
Mattia G. Bergomi
Can music be represented as a meaningful geometric and topological object? We propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the Tonnetz. The Tonnetz is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology to describe the persistent properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analysing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions. Keywords: Tonnetz, persistent homology, clustering 75 minutes talk, 45 minutes discussion.
16 Gen 2017
seminario interdisciplinare
Persistent homology as a musical fingerprint
Mattia G. Bergomi
Can music be represented as a meaningful geometric and topological object? We propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the Tonnetz. The Tonnetz is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology to describe the persistent properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analysing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions. Keywords: Tonnetz, persistent homology, clustering 75 minutes talk, 45 minutes discussion.
13 Gen 2017
seminario interdisciplinare
nell'ambito della serie
Neuromatematica
La corteccia parietale posteriore come crocevia tra il mondo visivo e quello somatosensoriale: percezione, organizzazione ed interpretazione
Michela Gamberini
10 Gen 2017
seminario di algebra e geometria
nel ciclo di seminari
Seminari di Algebra
La corrispondenza di Springer - Parte quarta
Luca Migliorini
Se W e' il gruppo di Weyl di un gruppo algebrico lineare semplice G, la corrispondenza di Springer fornisce una realizzazione geometrica delle sue rappresentazioni irriducibili e una loro parametrizzazione in termini di classi di coniugio degli elementi unipotenti di G (più dati ulteriori se il gruppo non è di tipo A). Tale parametrizzazione si basa su notevoli proprietà geometriche del cono nilpotente e di una sua desingolarizzazione naturale (la risoluzione di Springer). I seminari esporranno le linee principali di questa costruzione, esemplare in teoria geometrica delle rappresentazioni, seguendo un approccio dovuto principalmente a Kazhdan-Lusztig e Borho-Macpherson. Per semplicità ci concentreremo su gruppi di tipo A sul campo complesso.