Archivio 2018

24 Mag 2018
seminario interdisciplinare
Immersioni isometriche del piano iperbolico nello spazio di Minkowski.
Andrea Seppi
Lo spazio di Minkowski è l’analogo Lorentziano dello spazio Euclideo, ed è noto che esiste un’immersione isometrica del piano iperbolico nello spazio di Minkowski di dimensione 2+1, la quale è analoga all’immersione isometrica della sfera nello spazio Euclideo. A differenza del caso Euclideo, questa immersione isometrica non è unica a meno di isometrie globali. Presenterò alcuni risultati (i più recenti in collaborazione con Francesco Bonsante e Peter Smillie) sul problema della classificazione di tali immersioni isometriche, sottolineando le connessioni con altri argomenti, come le mappe armoniche tra varietà Riemanniane, le equazioni di Monge-Ampère e la teoria di Teichmüller.
24 Mag 2018
seminario di analisi numerica
Metodi numerici per Quantificazione dell'Incertezza di PDE con parametri aleatori
Lorenzo Tamellini
Quando si costruisce un modello matematico per descrivere il comportamento di un sistema fisico, si deve spesso affrontare il problema che alcuni parametri del modello (coefficienti, forzanti, condizioni al bordo, forma del dominio etc) non sono noti esattamente, ma al contrario sono affetti da un certo grado di incertezza, e quindi descritti in maniera naturale in termini di variabili aleatorie/campi aleatori. La necessita` di stimare l'affidabilita` delle simulazioni numeriche tenendo conto di tale aleatorieta` ha portato all'introduzione di tecniche di Quantificazione dell'Incertezza (Uncertainty Quantification) nel calcolo scientifico. Obiettivi classici di questo tipo di analisi sono a) il calcolo di indici statistici (ad es media e varianza) per quantita` di interesse legate alla soluzione dell'equazione considerata (ad esempio, il valore della soluzione in un punto, il suo integrale sul dominio di calcolo, o il flusso in uscita) b) il miglioramento della descrizione statistica dei parametri del modello basandosi su osservazioni sperimentali di tali quantita` di interesse. Il primo tipo di analisi e` tipicamente conosciuto come "Forward uncertainty Quantification", mentre il secondo "Inverse Uncertainty QUantification". Uno degli ostacoli principali in UQ e` rappresentato dal fatto che in molte applicazioni sono necessarie numerose variabili aleatorie (a volte dell'ordine di decine o centinaia) per ottenere rappresentazioni accurate dell'incertezza del modello. Gli schemi numerici adottati per eseguire l'analisi di UQ devono quindi essere tali da limitare il piu` possibile il peggioramento della performance quando il numero di parametri aumenta - un fenomeno noto come "curse of dimensionality". In questo seminario introdurro` le basi della metodologie di UQ per PDE con parametri aleatori e discutero` la loro applicazione a qualche problema (semplificato) di interesse ingegneristico (stampa 3d, flussi in mezzi porosi, bacini sedimentari)
22 Mag 2018
seminario di fisica matematica
nell'ambito della serie
Topics in Mathematics 2017/2018
A baby version of a crash course on some fundamentals of infinite ergodic theory (second part)
Marco Lenci
17 Mag 2018
seminario di analisi matematica
Formazione di singolarità nel moto secondo la curvatura media frazionaria
Carlo Sinestrari
Nel 2009, Caffarelli, Roquejoffre e Savin hanno introdotto una nozione non locale di perimetro di insiemi, detto perimetro frazionario. Dalla variazione prima del perimetro si ottiene la curvatura media frazionaria di un insieme, che è definita da un operatore integrale con nucleo singolare. Da allora, vari autori hanno studiato queste nozioni, ottenendo ad esempio proprietà di regolarità per superfici minime non locali, esistenza di superfici di tipo Delaunay a curvatura frazionaria costante, e disuguaglianze isoperimetriche. Più recentemente, è stato considerato il moto di superfici secondo la curvatura media frazionaria, che è il flusso gradiente del perimetro non locale, ottenendo risultati di esistenza e unicità per soluzioni deboli e proprietà di invarianza. Dopo aver richiamato queste proprietà, ci soffermeremo su un risultato in collaborazione con E. Cinti ed E. Valdinoci, che dimostra l'esistenza di superfici che sviluppano singolarità di tipo "collo di bottiglia" (neckpinch). E' interessante notare che, come conseguenza della natura non locale della curvatura frazionaria, tali singolarità si sviluppano in qualunque dimensione, inclusa quella orrispondente al caso di curve nel piano. In questo aspetto l'evoluzione si differenzia da quella classica, dove le curve si contraggono a un punto senza sviluppare singolarità in base al teorema di Grayson.
17 Mag 2018
seminario interdisciplinare
Professione Matematico
Elisa Bragaglia - Lucia Capecci - Jacopo Lanzoni - Enrico Manfredi - Sonia Solaroli
Durante il seminario cinque ex studenti di matematica, laureati negli ultimi anni, verranno a raccontare la loro esperienza nel mondo del lavoro. Sarà un’occasione per scoprire le reali possibilità occupazionali per un laureato in matematica, le difficoltà che al termine del percorso gli studenti si troveranno ad affrontare e le potenzialità che sono più apprezzate. I cinque giovani matematici faranno una breve presentazione sulla loro esperienza per poi lasciare spazio alle domande.
17 Mag 2018
seminario di fisica matematica
nell'ambito della serie
Topics in Mathematics 2017/2018
A baby version of a crash course on some fundamentals of infinite ergodic theory
Marco Lenci
16 Mag 2018
nel ciclo di seminari
Seminari di Probabilità
Existence of proper regular conditional distributions
Pietro Rigo
In the first part of the talk, mainly of the heuristic type, some basic notions (such as regularity, properness, disintegrability) are recalled and some examples are discussed. The second part is more technical and is devoted to some results and their implications. In the classical (Kolmogorovian) framework, a few 0-1 laws for regular conditional distributions are stated. Special attention is paid to the tail and the symmetric sigma- fields. In the coherent (de Finettian) framework, with reference to a Bayesian inferential problem, the existence of posterior distributions that make sufficient a given statistics, or make optimal a given estimator, is discussed. Finally, some compatibility problems for conditional distributions are mentioned, and a few asymptotic results are stated
16 Mag 2018
nel ciclo di seminari
Seminari di Probabilità
Existence of proper regular conditional distributions
Pietro Rigo (Università di Pavia)
In the first part of the talk, mainly of the heuristic type, some basic notions (such as regularity, properness, disintegrability) are recalled and some examples are discussed. The second part is more technical and is devoted to some results and their implications. In the classical (Kolmogorovian) framework, a few 0-1 laws for regular conditional distributions are stated. Special attention is paid to the tail and the symmetric sigma- fields. In the coherent (de Finettian) framework, with reference to a Bayesian inferential problem, the existence of posterior distributions that make sufficient a given statistics, or make optimal a given estimator, is discussed. Finally, some compatibility problems for conditional distributions are mentioned, and a few asymptotic results are stated
14 Mag 2018
seminario interdisciplinare
Geometric Deep Learning
A. Cattabriga
14 Mag 2018
seminario interdisciplinare
Geometric Deep Learning
A. Cattabriga
11 Mag 2018
seminario di finanza matematica, interdisciplinare
On Overconfidence, Bubbles and the Stochastic Discount Factor
Hye-Jin Cho, Université Paris 1 Panthéon-Sorbonne
This study is intended to provide a continuous-time equilibrium model in which overconfidence generates disagreements among two groups regarding asset fundamentals. Every agent in trading wants to sell more than the average stock price in the market. However, the overconfident agent drives a speculative bubble with a false belief that the stock price will tend to move to the average price over time. I represent the difference between a false belief and a stochastic stationary process which does not change when shifted in time. The gap of beliefs shows how to accommodate dynamic fluctuations as parameters change such as the degree of overconfidence or the information of signals. By showing how changes in an expectation operator affect the stochastic variance of economic fundamentals, speculative bubbles are revealed at the burst independently from the market.
10 Mag 2018
seminario di analisi matematica
Level convessita' e distanze intrinsiche nei problemi variazionali in L^\infty
Francesca Prinari
In questo seminario, dopo aver introdotto la nozione di level convessita' ed il ruolo che essa riveste nei problemi di Calcolo delle Variazioni in L^\infty, si studiera' l'inviluppo semicontinuo di un funzionale della forma $$F(u)=\supess_{\Omega} f(x,Du(x))$$ su $W^{1,\infty}(\Omega)$ rispetto la topologia debole* e si dimostrera' che esso soddisfa la proprieta' di level convessita'. A tal fine si rappresenteranno i sottolivelli del funzionale rilassato per mezzo di opportune pseudo-distanze associate al funzionale $F$.
10 Mag 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
Embeddings of graphs on​ surfaces and genus of groups
Michele Mulazzani
07 Mag 2018
seminario interdisciplinare
Modelli della corteccia visiva e Deep Learning
G. Citti
04 Mag 2018
seminario interdisciplinare
nel ciclo di seminari
Neuromatematica
Large scale cortical networks for controlling motor and cognitive motor functions
Borra Elena
Cortical functions result from the conjoint function of different, reciprocally connected areas working together as large-scale functionally specialized networks. Architectonic, connectional, and functional data have provided evidence for functionally specialized large-scale cortical networks of the macaque brain involving temporal, parietal, and frontal areas. These networks appear to play a primary role in controlling different aspects of motor and cognitive motor functions, such as hand action organization and recognition, or oculomotor behavior and gaze processing. Based on comparison of these data with data from human studies, it is possible to argue that there is clear evidence for human counterparts of these networks. These human and macaque putatively homologue networks appear to share phylogenetically older neural mechanisms, which in the evolution of the human lineage could have been exploited and differentiated resulting in the emergence of human-specific functions higher-order cognitive functions
03 Mag 2018
seminario di analisi matematica
Degenerate Differential Problems with Fractional Derivatives.
Angelo Favini
03 Mag 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
A few topics in graph theory
Marilena Barnabei
30 Apr 2018
seminario di algebra e geometria
Universal calculus on quantum principal bunlde
Alessandro Zampini
26 Apr 2018
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2017/2018
Control and observability on tori (part 2)
Maciej Zworski (Berkeley University)
I will use time dependent Schroedinger equation on the two dimensional torus as a ``laboratory" for describing control and observability for time dependent PDE. The plan of the lectures is 1. General description of the problem and Lions's argument for the equivalence of observability and control. 2. Introduction to semiclassical methods and defect measures. 3. Control by non-empty open sets on tori (a proof of now classical results of Haraux, Jaffard and Komornik using defect measures). 4. A review of modern advances: control by sets of positive Lebesgue measure (Bourgain--Burq--Z, Burq--Z), control on discs (Anantharaman--Leautaud--Macia), control by non-empty open sets on hyperbolic surfaces (Bourgain--Dyatlov, Dyatlov--Jin, Jin).
26 Apr 2018
seminario di analisi numerica
SemiDefinite Programming problem. Introduzione al problema e primi aspetti computazionali.
Margherita Porcelli
24 Apr 2018
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2017/2018
Control and observability on tori (part 1)
Maciej Zworski (Berkeley University)
I will use time dependent Schroedinger equation on the two dimensional torus as a ``laboratory" for describing control and observability for time dependent PDE. The plan of the lectures is 1. General description of the problem and Lions's argument for the equivalence of observability and control. 2. Introduction to semiclassical methods and defect measures. 3. Control by non-empty open sets on tori (a proof of now classical results of Haraux, Jaffard and Komornik using defect measures). 4. A review of modern advances: control by sets of positive Lebesgue measure (Bourgain--Burq--Z, Burq--Z), control on discs (Anantharaman--Leautaud--Macia), control by non-empty open sets on hyperbolic surfaces (Bourgain--Dyatlov, Dyatlov--Jin, Jin).
19 Apr 2018
seminario di analisi matematica
Stime quantitative per ipersuperfici a curvatura media quasi costante
Giulio Ciraolo
Discuteremo alcune versioni quantitative del Teorema di Alexandrov della bolla di sapone, che afferma che le sfere sono le sole ipersuperfici chiuse embedded a curvatura media costante. In particolare, considereremo ipersuperfici con curvatura media vicina ad una costante e descriveremo in maniera quantitativa la vicinanza ad una singola sfera o ad una collezione di sfere tangenti di raggio uguale in termini dell'oscillazione della curvatura media. Inoltre considereremo il problema analogo in ambito nonlocale, mostrando come l'effetto nonlocale implichi una maggiore rigidità del problema e prevenga la formazione di più bolle.
19 Apr 2018
seminario interdisciplinare
Detecting and measuring bias in online platforms: A Network Science approach
Giacomo Livan
The last few years have witnessed the rise of the Sharing Economy, a collection of decentralized online platforms whose users exchange knowledge, goods, and resources on a peer-to-peer basis. Sharing Economy platforms are often praised for their meritocratic approach, where all participants, regardless of their gender or ethnicity, receive the same opportunities to emerge through digital peer review mechanisms. Yet, they have recently come under fire due to reports of discriminatory behaviours and manipulations of their reputation systems. This raises an important question: are Sharing Economy platforms fair marketplaces, where all participants operate on a level playing field, or are they large-scale online aggregators of offline human biases? In this talk I will address this question on a number of examples, showing how online platforms can be represented in terms of networks, and how this allows to detect and measure some of the biases that might affect their users' behaviour. In particular, I will present clear evidence of avoidance between users from different ethnic backgrounds on Airbnb, and I will show how user reputation scores are distorted by the widespread practice of reciprocating highly positive ratings in a variety of platforms. I will conclude by discussing how these findings can be used to provide platform design recommendations, aimed at exposing and possibly reducing the biases we detect, in support of a fairer and more inclusive growth of Sharing Economy platforms.
18 Apr 2018
seminario di fisica matematica, probabilità
Refinements of the Central Limit Theorem and Large Deviation Principles for weakly dependent random variables
Kasun Fernando (U. of Maryland, USA)
We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the Central Limit Theorem and Large Deviation Principles for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. We primarily use spectral techniques to obtain these results.The work on CLT is joint with Carlangelo Liverani (Rome) and the work on LDPs is joint with Pratima Hebbar (Maryland).
17 Apr 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
An ongoing research about the persistent homology of vector-valued functions
Patrizio Frosini
In this talk we will illustrate a new line of research concerning the persistent homology of regular functions from a closed manifold to R^2. In particular, we will describe the phenomenon of monodromy for 2D persistence diagrams, and a recent mathematical model based on the concepts of extended Pareto grid and coherent transport of matchings. Some new theoretical results and open problems will be presented.
17 Apr 2018
seminario di analisi matematica, analisi numerica, probabilità
Infimal convolution of data discrepancies for mixed noise removal
Luca Calatroni
In several real-word imaging applications such as microscopy, astronomy and medical imaging, transmission and/or acquisition faults result in a combination of multiple noise statistics in the observed image. Classical data discrepancies models dealing with this scenario linearly combine standard data fidelities used for single-noise removal or consider exact log-likelihood MAP estimators which are difficult to deal with in practice. In this talk, we derive a statistically consistent variational model for combining mixed data fidelities associated to single noise distributions in a handy infimal convoution fashion by which individual noise components in the data are modelled appropriately and separated from each other after a Total Variation smoothing. Our analysis is carried out in function spaces. For the numerical solution of the resulting denoising model, we propose a semismooth Newton-type scheme and show preliminary results in the context of bilevel learning for blind mixed denoising.
13 Apr 2018
seminario di fisica matematica
Variational problems in disordered systems and applications to mean field models
Francesco Guerra
We will discuss some recent results and perpsectives on mean field disordered models.In particular we will focus on convexity properties of bipartite spin glasses
12 Apr 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
An introduction to representation theory (part 2)
Fabrizio Caselli
In these lectures the basic notions (such as irreducibility, complete reducibility, indecomposability, induction…) of representation theory are introduced. We will develop the theory following basic examples of finite groups, algebraic groups, associative algebras, Lie algebras and quivers, focusing on similarities and discrepancies.
10 Apr 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
A gentle introduction to the use of G-invariant persistent homology for topological data analysis
Patrizio Frosini
In this talk we will present a metric approach to topological data analysis that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions. These functions represent the set of data that are accessible to the observer, while the operators describe the way the observer elaborates the data and enclose the invariance that he/she associates with them. In particular, we will illustrate the concept of G-equivariant non-expansive operator and how it can be used to build G-invariant persistent homology. The exposition will remain at an elementary and non-technical level, limiting itself to a description of the main ideas in our mathematical setting.
05 Apr 2018
seminario di analisi matematica
The measure and the structure of the free boundary in the lower dimensional obstacle problem
Matteo Focardi (U. Firenze)
In this talk I present the main results of a recent paper in collaboration with E. Spadaro (U. Roma La Sapienza) on the regularity of the free boundary for a class of lower dimensional obstacle problems, including the classical scalar Signorini problem. We prove the first results concerning the global structure of the free boundary, in particular showing its local finiteness and its rectifiability.
05 Apr 2018
seminario di algebra e geometria
nell'ambito della serie
Topics in Mathematics 2017/2018
An introduction to representation theory (part 1)
Fabrizio Caselli
In these lectures the basic notions (such as irreducibility, complete reducibility, indecomposability, induction…) of representation theory are introduced. We will develop the theory following basic examples of finite groups, algebraic groups, associative algebras, Lie algebras and quivers, focusing on similarities and discrepancies.
30 Mar 2018
nel ciclo di seminari
Neuromatematica
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30 Mar 2018
seminario di analisi matematica
Elliptic regularity for ultraparabolic equations
Cyril Imbert, CNRS, Ecole normale supérieure, département de mathématiques et applications
29 Mar 2018
seminario di algebra e geometria
A global Torelli theorem for singular symplectic varieties
Christian Lehn
Verbitsky's Global Torelli theorem has been one of the most important advances in the theory of holomorphic symplectic manifolds in the last years. In a joint work with Ben Bakker (University of Georgia) we prove a version of the Global Torelli theorem for singular symplectic varieties and discuss applications. Symplectic varieties have interesting geometric as well as arithmetic properties, their birational geometry is particularly rich. Our results are obtained through the interplay of Hodge theory, deformation theory, and a further example of Verbitsky's technique which might go under the name "how to deduce beautiful consequences from ugly behavior of moduli spaces".
29 Mar 2018
nell'ambito della serie
GHAIA Seminars
Bubbles: symmetries, deformations and an application to monodromy of ODEs.
Lorenzo Ruffoni
Complex projective structures with branch points arise naturally in the study of a certain class of linear rank 2 ODEs on Riemann surfaces. We focus on the genus 2 case, where these structures can be conveniently described in terms of bubbling, i.e. connected sum with the Riemann sphere. This geometric point of view allows for an effective description of the symmetries and deformations of these geometric structures. We will present an application to the study of the Riemann-Hilbert map for the aforementioned class of ODEs.
27 Mar 2018
seminario di analisi matematica
Rigidity and stability results for the Gauss mean value formula
Giovanni Cupini
The mean integral of harmonic functions on balls centered at x equals the value of these functions at x. This is the well known Gauss mean value theorem. In 1972 Kuran proved the reverse: if D is a bounded open set containing x, such that the mean integral of harmonic functions on D equals the value of these functions at x, then D is a ball centered at x. Two questions may be raised: (1) similar rigidity results can be proved for weighted mean integrals? (2) is the Gauss mean value formula stable? That is: if the mean integral of harmonic functions on D centered at x is almost equal to the value of these functions at x, then D is almost a ball with center x? In this talk I will discuss recent results on these issues obtained in collaboration with E. Lanconelli (1) and with N. Fusco, E. Lanconelli and X. Zhong (2)
27 Mar 2018
seminario di analisi matematica
Partial regularity of minimizers for real-analytic sub--Riemannian metrics
Paolo Albano
We describe the problem of the regularity of sub-Riemannian minimizers. We give some regularity results, in the real-analytic framework, obtained in collaboration with A.Bove.
27 Mar 2018
seminario di analisi matematica
Symmetry results for hinged and clamped composite plate problems
Eugenio Vecchi, Sapienza Università di Roma
27 Mar 2018
seminario di analisi matematica
On the electrostatic Born-Infeld equation with point charges
Francesca Colasuonno, Università di Torino
In this seminar I will present some results on the electrostatic Born-Infeld equation set in the whole R^n. This equation is governed by the Lorentz-Minkowski mean curvature operator and was introduced, in the theory of nonlinear electromagnetism, as a generalization of the Poisson equation for the electrostatic potential. I will consider the case of a superposition of (possibly non-symmetrically distributed) point charges and discuss sufficient conditions to guarantee that the minimizer of the action functional is a solution of the problem. I will also present an approximation of the considered problem, governed by a sum of 2m-Laplacians, and show some qualitative properties of the approximating solutions, such as their behavior near the charges. This is a joint work with Denis Bonheure (Université Libre de Bruxelles) and Juraj Foldes (University of Virginia) available at arXiv:1707.07517.
27 Mar 2018
seminario di analisi matematica
Towards a Faber-Krahn inequality for the truncated Laplacian
Isabeau Birindelli, Sapienza Università di Roma
Abstract: We shall see how symmetry plays a role on the estimates of the principal eigenvalue. We shall briefly recall some results for the Pucci operators and then show some new surprising results for the Harvey Lawson truncated laplacian. We shall also see some applications concerning the regularity of solutions in domains which are convex but not strictly convex.
27 Mar 2018
seminario di analisi matematica
Some classification results for stable solutions to some nonlocal problems
Eleonora Cinti
In this talk we present some recent results concerning the classification of stable solutions to some semilinear nonlocal problems, such as the fractional Allen-Cahn equation. Crucial ingredients in the proof of the main results will be given by density and energies estimates for stable solutions.
27 Mar 2018
seminario di analisi matematica
Symmetry and rigidity properties for long-range phase coexistence models
Enrico Valdinoci, Università Statale di Milano
We discuss some recent results on nonlocal phase transitions modelled by the fractional Allen-Cahn equation, also in connection with the surfaces minimising a nonlocal perimeter functional. In particular, we consider the "genuinely nonlocal regime" in which the diffusion operator is of order less than 1 and present some rigidity and symmetry results.
27 Mar 2018
seminario di analisi matematica
Harnack inequalities of Landis-type for Hörmander operators in non-divergence form
Giulio Tralli, Sapienza Università di Roma
In this talk we will discuss the validity of Harnack inequalities for two classes of linear second order equations in nondivergence form. The first class is formed by degenerate-elliptic operators which are horizontally elliptic with respect to Heisenberg-type vector fields. The second one constitutes a class of evolution operators of Kolmogorov-Fokker-Planck type. The analogous of the Krylov-Safonov Harnack inequality for these classes of Hörmander operators with bounded measurable coefficients is still unknown, due to the absence of proper Aleksandrov-Bakelman-Pucci type estimates. We will show a perturbative approach to prove invariant Harnack inequalities for operators with coefficients satisfying either a Cordes-Landis assumption or a continuity hypothesis. This talk is based on joint works with F. Abedin and C.E. Gutiérrez.
27 Mar 2018
seminario di analisi matematica
A nonlinear toy model in kinetic theory
Cyril Imbert, CNRS, Ecole normale supérieure, département de mathématiques et applications
In this talk, I will present a recent joint work with C. Mouhot. It concerns a toy non-linear model in kinetic theory. We will see that the problem is globally well-posed in Sobolev spaces. The construction of solutions rely on some recent Hoelder estimates obtained with F. Golse, C. Mouhot and A. Vasseur combined with appropriate Schauder estimates.
26 Mar 2018
nell'ambito della serie
GHAIA Seminars
Seminario Deep Learning
R. Fioresi
23 Mar 2018
seminario di analisi matematica
The Faber-Krahn inequality
Lorenzo Brasco (Università di Ferrara)
Among N-dimensional open sets with given measure, balls (uniquely) minimize the first eigenvalue of the Laplacian with homogeneous Dirichlet boundary conditions. We review this classical result and discuss some of its applications. Then we show how this can be enhanced by means of a quantitative stability estimate. The resulting inequality, first conjectured by Nadirashvili and Bhattacharya & Weitsman, is sharp. The results presented are contained in a paper in collaboration with Guido De Philippis and Bozhidar Velichkov.
22 Mar 2018
nell'ambito della serie
Colloquio di Dipartimento
Hamming cube, martingales, Monge-Amp\’ere, and ancient solutions of heat equation
Alexander Volberg
Harmonic analysis is intimately related with martingale estimates. But there is another type of discrete analysis, namely, harmonic analysis on Hamming cube (the math. foundation of Big Data science) that seemed to be disjoint from this relationship. We show how many classical (and some new) estimates on Hamming cube follow from martingale estimates. We also show why this is related to solving certain non-linear PDE of Monge--Amp\`ere type and what are the relations with classical inequalities in Gaussian spaces. Our Monge—Amp\’ere equation will naturally bring us to ancient solutions of heat equation. On Hamming cube Monge—Amp\’ere should be discretized accordingly. But how? There are so many different ways to discretize PDE. We will show one way that seems to be often the right one and that ties harmonic analysis estimates of martingales with Poincar\’e type estimates on Hamming cube.
22 Mar 2018
seminario di analisi matematica
nell'ambito della serie
Topics in Mathematics 2017/2018
Sums of closed operators and L^p-maximal regularity for abstract parabolic equations (part 2)
Alberto Venni
The maximal regularity in L^p (1<p<∞) for the solution of a linear abstract Cauchy problem (1) u'(t) + Lu(t) = f(t), (2) u(0) = 0 where the unknown function u and the given function f are defined on [0,T] with values in a Banach space X, is the requirement that for any f∈L^p(0,T ; X) the Cauchy problem (1) - (2) has a unique solution and that u' and Au belong to L^p(0,T; X) and depend continuously on f in L^p(0,T; X). This problem can be stated in a more abstract form as the problem of solving the equation Au + Bu = f in the space Y = L^p(0,T; X) for appropriate operators A and B acting in Y. In these two seminars I will speak of a result that gives conditions on A, B and X to ensure the bounded invertibility of the operator A+B, and hence the maximal regularity for the solutions of the Cauchy problem.
16 Mar 2018
seminario di algebra e geometria
nell'ambito della serie
Seminari BAD
Philosophical 3-folds: how Tom and Jerry became existentialists
Enrico Fatighenti
The history of philosophy is full of deep and unanswered questions. Who are we? What is our purpose in this world? How many QQ-Fano threefolds exist in high codimension? Prophets Mori and Mukai in the late 80s provided a classification of smooth Fano threefolds of index one, and their 17+88 families are an irreplaceable tool in every birational geometer working kit. More important than the list itself was the strategy (the 'vector bundle method') and the mantra: Fano threefolds arise as linear section of "good" varieties coming from representation theory. The same results sadly does not extends to the QQ-Fano threefolds case (the natural playground for MMPers). Tom and Jerry models provides a good level of understanding up to codimension three, but the garden is still wild and untamed. In this talk we will provide an overview of the subject, and we will report on some recent progress in the classification.
16 Mar 2018
seminario interdisciplinare
nell'ambito della serie
Neuromatematica
Integrazione visuomotoria: l’area V6A della corteccia di macaco e i movimenti del braccio
Rossella Breveglieri
16 Mar 2018
nel ciclo di seminari
Geometria Algebrica e Tensori
Algebraic boundaries among typical ranks for real binary forms
Chiara Brambilla
Binary real forms of degree d admit as typical ranks all the integers between floor(d/2)+1 and d. We investigate the boundary between the open subset of rank r forms and the open subset of rank r+1. These boundaries are known only in the extreme cases, by Lee-Sturmfels (between rank floor(d/2)+1 and floor(d/2)+2) and Comon-Ottaviani (between rank d-1 and d). We investigate the intermediate boundaries. In the talk I will present our new results, focusing on the case of degree 7 forms. This is work in progress with G.Stagliano'.
15 Mar 2018
seminario di analisi matematica
Everywhere regularity of vectorial minimizers of some non-convex functionals
Giovanni Cupini
The convexity of the integrand of a functional of the calculus of variations is equivalent to the lower semicontinuity of the functional in the scalar case, but it is only a sufficient condition in the vectorial case. So, it is not satisfied by many interesting examples to which the existence theorems apply. Moreover, the convexity of the integrand turns out to be a too strong and unrealistic assumption in applications, as for instance in mathematical models in nonlinear elasticity (Ball 1977). In the vectorial framework more appropriate and weaker conditions than the convexity are the polyconvexity and the quasiconvexity. Under these assumptions, many results were proved concerning the partial regularity of minimizers (regularity on open sets of full measure), but the results concerning the everywhere regularity are very few and mainly in low dimensions (n=N=2). We will discuss recent everywhere regularity results of vectorial minimizers for some classes of polyconvex and quasiconvex functionals (n,N >2) obtained in collaboration with F. Leonetti and E. Mascolo (local boundedness) and with them and M. Focardi (Holder continuity). The proofs rely on the power and elegant (typically scalar) method by De Giorgi (1957).
15 Mar 2018
seminario di analisi matematica
nell'ambito della serie
Topics in Mathematics 2017/2018
Sums of closed operators and L^p-maximal regularity for abstract parabolic equations (part 1)
Alberto Venni
The maximal regularity in L^p (1<p<∞) for the solution of a linear abstract Cauchy problem (1) u'(t) + Lu(t) = f(t), (2) u(0) = 0 where the unknown function u and the given function f are defined on [0,T] with values in a Banach space X, is the requirement that for any f∈L^p(0,T ; X) the Cauchy problem (1) - (2) has a unique solution and that u' and Au belong to L^p(0,T; X) and depend continuously on f in L^p(0,T; X). This problem can be stated in a more abstract form as the problem of solving the equation Au + Bu = f in the space Y = L^p(0,T; X) for appropriate operators A and B acting in Y. In these two seminars I will speak of a result that gives conditions on A, B and X to ensure the bounded invertibility of the operator A+B, and hence the maximal regularity for the solutions of the Cauchy problem.
15 Mar 2018
seminario di analisi numerica
metodi numerici per sistemi di equazioni matriciali
Sarah Gaaf
13 Mar 2018
Reti neurali e Deep Learning
R. Fioresi
13 Mar 2018
seminario di fisica matematica
Propagation of singularities at a non analytic hyperbolic fixed point and an application to the quantization of resonances II
Setsuro FUJIIE
We will explains some details of the proof of the previous seminar, concerning the quantization rule of resonances when the trapped set of the corresponding Hamiltonian system consists of hyperbolic fixed points and associated homoclinic and heteroclinic trajectories. (joint work with Jean-Fran¥c cois Bony (Bordeaux), Thierry Ramond (Paris XI) and Maher Zerzeri (Paris XIII)).
09 Mar 2018
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
s-Regular Functions which Preserve a Complex Slice
Chiara De Fabritiis
Regular functions on the skew-field of quaternions were introduced by Gentili and Struppa some 10 years ago in order to give an analogue of holomorphic functions in a non commutative setting. After a (short) introduction, I will give a formula which allows us to simplify the understanding of the *-product, which corresponds to the pointwise product of holomorphic functions. The peculiar structure of quaternions, foliated in copies of complex plane, drives naturally to consider the classes of functions which preserve either one or all complex slices. The main part of the talk will be devoted to characterize the functions whose sum, *-product or conjugate preserve a slice. At the end, I will address to the case of *-powers which shows an unexpected connection with a problem of algebraic geometry studied by Causa and Re. (Joint work with A. Altavilla)
08 Mar 2018
Carleson measures for the Dirichlet space on the polydisc
Pavel Mozolyako
The Dirichlet space on the polydisc consists of analytic functions defined on the cartesian product of n-copies of a disc, having finite Sobolev norm. In the one-dimensional case (d = 1) the Carleson measures were first described by Stegenga (’80) in terms of capacity, further development was achieved in papers by Arcozzi, Rochberg, Sawyer, Wick and others. Following Arcozzi et al. we consider the equivalent problem in the discrete setting - characterization of trace measures for the Hardy operator on the polytree. For d = 2 we present a description of such measures in terms of bilogarithmic capacity (which, in turn, gives the description of Carleson measures for the Dirichlet space on the bidisc in the sense of Stegenga). We also discuss some arising combinatorial problems. This talk is based on joint work with N. Arcozzi, K.-M. Perfekt, G. Sarfatti.
08 Mar 2018
seminario di analisi matematica, fisica matematica
Propagation of singularities at a non analytic hyperbolic fixed point and an application to the quantization of resonances I
Setsuro FUJIIÉ (Ritsumeikan University, Kyoto)
It is well known as Hörmander's theorem that the (semiclassical) wave front set of the solution to a pseudo-differential equation propagates along Hamiltonian flows of the real principal type symbol. We extend this theorem to fixed points of the Hamiltonian vector field. To a hyperbolic fixed point, associated an outgoing and an incoming stable manifolds, and we show that if the semiclassical wave front set is empty on the incoming stable manifold (except at the fixed point), then it is also empty on the outgoing one. We also show how such theorems are applied to a scattering problem of the Schr¥"odinger operator. We give the quantization rule of resonances when the trapped set of the corresponding Hamiltonian system consists of hyperbolic fixed points and associated homoclinic and heteroclinic trajectories. This is a joint work with Jean-Fran¥c cois Bony (Bordeaux), Thierry Ramond (Paris XI) and Maher Zerzeri (Paris XIII)
01 Mar 2018
seminario interdisciplinare
nell'ambito della serie
Colloquio di Dipartimento
Some equations of biology
Benoit Perthame
28 Feb 2018
seminario di probabilità
Probabilità e Informazione
Davide Dardari, Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi"
26 Feb 2018
seminario di algebra e geometria
Reti neurali convoluzionali e Deep Learning
R. Fioresi
L'intenzione e' di discutere le note di Fei Fei Li: http://cs231n.stanford.edu/ [cs231n.stanford.edu] Non sono necessari requisiti particolari eccetto qualche conoscenza di programmazione, preferibilmente python.
22 Feb 2018
seminario di analisi matematica
Poincaré-Sobolev Inequalities and the p-Laplacian
Scott Rodney
20 Feb 2018
seminario di fisica matematica
Focusing Belief Propagation: traffic slowdowns prediction.
Rachele Luzi
Belief Propagation (BP) is an iterative message passing algorithm that can be used to derive marginal probabilities on a system within the Bethe-Peierls approximation. It is not well understood how this deep learning method is able to learn and how it doesn't get trapped in configurations with low computational performance. Since we aim to classify the congestion situations, we analyze the fundamental diagram of traffic which gives a relation between the traffic flow and the traffic density. A traffic congestion occurs when the density of the road grows up and the flow decreases. In order to predict congestion situations, we train the BP neural network using binarized vectors obtained by the processing of the fundamental diagram. We apply our method to real data which have been recorded by traffic detectors provided by Emilia Romagna region.
20 Feb 2018
seminario di fisica matematica
Dreaming and unlearning in neural networks
Elena Agliari
In the first part of this talk we review the main definitions, concepts and classical results on neural networks, distinguishing between the two principal cognitive tasks, i.e., "learning" and "retrieval". Focusing on the latter, the Hopfield model is probably the one most extensively investigated, although it exhibits an intrinsic capacity limit (in terms of the ratio between the amount P of stored patterns and the network size N) far below the theoretical known bound. In this talk we will show that this limit can be improved by means of “unlearning” iterations which mimic unconscious mechanisms taking place during the REM phase of mammals.
20 Feb 2018
seminario di fisica matematica
Mean field models and inverse problem
Cecilia Vernia
The inverse problem is tested for a class of statistical mechanics mean-field models: the Curie-Weiss model together with its multi-species version and the monomer-dimer model with attractive interaction. In particular, we show that the inversion is obtained by analytically identifying the model parameters in terms of the correlation functions. Moreover, we show that the robustness of the inversion procedure depends on the knowledge of the phase space of the system.
20 Feb 2018
seminario di analisi numerica
Convexity in Bipartite Mean Field models
Emanuele Mingione
Abstract In this talk we introduce a new variational approach to a class mean-field models, the so called bipartite spin models. In this framework the set of spins is divided in two groups and the interaction links only spins belonging to different groups. We start with the bipartite Curie-Weiss model showing how this approach leads to two equivalent variational representations of the limiting pressure density of the model.
20 Feb 2018
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2017/2018
An introduction to Neural Networks and Deep Learning
Andrea Asperti (Dipartimento di Informatica - Scienza e Ingegneria, Università di Bologna)
16 Feb 2018
nell'ambito della serie
Complex Analysis Lab
Some results on an isoperimetric model for charged liquid drops
Berardo Ruffini
We consider an isoperimetric model, originally proposed by Lord Rayleigh, aimed to describe the (lack of) equilibria of a liquid conducting drop in presence of a charge on its surface. The resulting functional contains an attracting term, usually modeled by the perimeter of the drop, and a repulsive term depending on the amount of charge considered and the electric capacity of the drop. We show that, quite surprisingly, the resulting variational problem is ill posed. We then consider several modification of it and we investigate existence, uniqueness and stability issues about those problem. The talk is based on works in collaborations with M. Goldman, C. Muratov and M. Novaga.
15 Feb 2018
seminario di analisi matematica
La tecnica della funzione massimale sharp nelle stime a priori W^{2,p} per operatori non variazionali
Marco Bramanti
10 Feb 2018
Propagation of singularities at a non analytic hyperbolic fixed point and an application to the quantization of resonances II
Set
08 Feb 2018
seminario di analisi matematica
Esponenti critici e dove trovarli
Sandra Lucente
In this talk I will present different semilinear wave-type problems with time-variable coefficients. Main discussion will concern the influence of such coefficients on the critical exponents which characterize the equation. The analysis of global existence and blow-up below or above this critical exponent will follows.
02 Feb 2018
seminario di algebra e geometria
Real forms of Kac Moody superalgebras, II
Meng Kiat Chuah
01 Feb 2018
seminario di analisi matematica
Il problema della regolarità delle geodetiche per le distanze di controllo.
Roberto Monti
Illustreremo una serie di risultati in collaborazione con vari coautori sul problema della regolarità delle curve minime per la lunghezza negli spazi di Carnot-Caratheodory. Discuteremo l'esistenza di tangenti in ogni punti a valcuni risultati algebrici sulle cosiddette curve abnormali.
27 Gen 2018
seminario di analisi matematica
Some random walks in the Heisenberg group
Juan Manfredi
We will discuss some examples of random walks and their relation to asymptotic mean value properties, and viscosity solutions to p-Laplace equations in the Heisenberg group.
26 Gen 2018
seminario di analisi matematica
nell'ambito della serie
Complex Analysis Lab
Shift invariant subspaces of the quaternionic space of slice L^2 functions
Giulia Sarfatti
In this seminar I will introduce the space of slice L^2 functions over the quaternions and I will present a characterization result for (simply and doubly) invariant subspaces for the shift operator, recently obtained in collaboration with Alessandro Monguzzi. Besides its own interest, our result gives a different proof for the quaternionic analog of the classical Beurling Theorem and allows us to obtain an inner-outer factorization for functions in the quaternionic Hardy space.
26 Gen 2018
seminario di analisi matematica
Mathematics of visual perception: a neurogeometrical approach
Alessandro Sarti
I will review the role of sub-Riemannian geometry in neurogeometry of the visual cortex (SE(2) group) and show how it is engendering visual perception. Particularly horizontal curves and geodesics will account for a number of geometric phenomena on the visual field. A mean field equation defined on the SE(2) geometry will model neural activity and its symmetry breaking will provide visual percepts. An open problem about heterogeneous neurogeometry will be preliminarily discussed. (Joint work with Giovanna Citti)
26 Gen 2018
seminario di analisi matematica
The restriction of the Fourier transform to surfaces: the hyperbolic case
Ana Vargas
The problem of restriction of the Fourier transform to hypersurfaces was posed by Stein in the seventies. This operator, in its adjoint form, gives the solution of dispersive equations (Schrödinger, wave, etc) in terms of the Fourier transform of the initial data. There are many open problems about dispersive equations for which it can be a powerful tool. Also, the restriction operator can be thought as a model case for more complicated oscillatory integral operators, such as, for instance, the operators of spherical summation of the Fourier transform. We will make a review of the problem, which is still open. We will present some new results for the case of surfaces with negative curvature. This part is joint work with Detlef Müller and Stefan Buschenhenke.
25 Gen 2018
seminario di algebra e geometria
Inner and outer automorphisms in Lie theory
Meng Kiat Chuah
For an algebraic or geometric object L, its automorphisms form a group Aut(L). If in addition Aut(L) has a topology, we denote its identity component by Int(L), and define the quotient group Out(L) = Aut(L)/Int(L). The members of Int(L) are called inner, and the remaining are called outer. Let L be a complex semisimple Lie algebra with Dynkin diagram D. It is well known that Out(L) = Aut(D). We extend this result to the real forms of L, and discuss the classification of real forms up to Int(L). We also consider possible extensions of these results to contragredient Lie superalgebras.
24 Gen 2018
seminario di analisi matematica
Minimal surfaces in the Heisenberg group
Sebastiano Nicolussi Golo
Geometric Measure Theory in the sub-Riemannian Heisenberg group leave unanswered several fundamental questions. The main issue is the regularity of area-minimizing surfaces, because sets of finite sub-Riemannian perimeter may have fractal behaviours. I will present some recent results obtained in collaboration with Francesco Serra Cassano and Manuel Ritoré.
24 Gen 2018
seminario di probabilità
On Wong - Zakai approximation theorems for Ito stochastic differential equations
Alberto Lanconelli, Università degli Studi di Bari
24 Gen 2018
seminario di analisi matematica
Celebrating two old friends: Juan Manfredi and the p-Laplacian
Giuseppe Mingione
As a young Ph.D. student, the first nonlinear operator I met was the p-Laplacean; later on, the first visitor I invited to Parma was Juan Manfredi (in 1997, if I remember correctly). And it is definitely not by chance the two things are related. This talk is the occasion to celebrate both of them, with some recent regularity results coming form nonlinear potential theory.
24 Gen 2018
seminario di analisi matematica
Poincaré inequalities for differential forms on Heisenberg groups
Pierre Pansu
Every closed differential form \omega on a Euclidean ball has a primitive whose L^q norm is bounded by the L^p norm of \omega (for suitable exponents p and q). We prove an analogous result for Rumin's exterior differential on Heisenberg balls. This is used to prove vanishing of \ell^{q,p}-cohomology of Heisenberg groups. Extension to other Carnot groups will be discussed.
22 Gen 2018
seminario di algebra e geometria
Real forms of Kac Moody superalgebras, I
M.-K. Chuah
22 Gen 2018
seminario di analisi matematica
Tug of war and nonlinear operators
Juan Manfredi, Pittsburgh University
Seminario riservato ai membri del progetto MANET
19 Gen 2018
seminario di algebra e geometria
nel ciclo di seminari
Seminari di Algebra
Equazioni differenziali con singolarita` di tipo oper e prodotto tensore di rappresentazioni
Andrea Maffei
Lo spazio degli Oper regolari e` una famiglia di equazioni differenziali lineari in una variabile complessa t, dipendenti da un parametro x con una singolarita` in t=x, associati ad un gruppo compatto connesso G. Nel caso di G=SL(2) nel seminario verranno introdotte e studiate delle famiglie di equazioni differenziali dipendenti da due parametri x,y con singolarita` in t=x e t=y e che per x diverso da y sono oper regolari vicino a x e vicino a y e verra` determinato il tipo di equazioni che si ottiene per x=y. I risultati descritti sono parte di un progetto di ricerca in collaborazione con Giorgia Fortuna.
19 Gen 2018
seminario di algebra e geometria
Tensori di Grassmann in Computer Vision
Cristina Turrini (Università di Milano)
Vengono introdotti i tensori di Grassmann per proiezioni P^k - - -> P^h_j, j=1,...r, utilizzati in Computer Vision per la ricostruzione proiettiva di scene statiche e dinamiche. Dopo aver ricordato i risultati classici (ossia nel caso di proiezioni da P^3), si considera il caso di due proiezioni tra spazi di dimensione qualsiasi e si accenna a qualche risultato per piu' proiezioni tra spazi di dimensione "piccola". I tensori di Grassmann vengono poi utilizzati per lo studio dei luoghi critici per la ricostruzione.
12 Gen 2018
seminario di analisi matematica
SL(n) - connections and self-adjoint difference operators on two-dimensional manifolds.
P.G. Grinevich
There are two alternative definitions of discrete connections on triangulated manifolds. The most known one associates a group element to each edge. An alternative approach uses first-order operators on simplexes of higher dimension. We show that in dimension two such connections are associated with self-adjoint second order operators, and the self-adjointness is equivalent to existence of two factorizations. We also show that Laplace transformations can be interpreted as the star-triangle transformation used in electrical circuits.
09 Gen 2018
seminario di analisi matematica
The nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects
P.G. Grinevich
In contrast with 1+1 dimensional systems, integrable 2+1 systems are usually non-local, and integration based on the scattering transform corresponds to a special choice of integration constants. For the KP equation this study turned out to be rather non-trivial. We show that in case of the so-called Pavlov equation, with is a dispersionless 2+1 dimensional integrable model, the answer can be explained using some lemma from integral geometry.
09 Gen 2018
seminario di algebra e geometria
Tori compatti associati a varieta' iperkaehler di tipo Kummer
Kieran O'Grady
Se X e' una varieta' iperkaehler di tipo Kummer, il gruppo di coomologia H^3(X) ha dimensione 8, e quindi la Jacobiana intermedia J^3(X) e' un toro complesso compatto di dimensione 4, proiettivo se X e' proiettiva. Faro' vedere come ricostruire esplicitamente J^3(X) a partire dalla struttura di Hodge su H^2(X). In particolare seguira' che, se X e' proiettiva, allora J^3(X) e' una varieta' abeliana di tipo Weil. Lo studio di J^3(X) suggerisce come (tentare di) costruire famiglie esplicite localmente complete di varieta' iperkaehler di tipo Kummer proiettive.
08 Gen 2018
seminario di algebra e geometria
COHEN-MACAULAY SIMPLICIAL COMPLEXES IN ARBITRARY CODIMENSION
RAHIM ZAARE-NAHANDI (UNIVERSITY OF TEHRAN)
A simplicial complex of dimension d - 1 is said to be Cohen-Macaulay in codimension t, 0 <= t <=d -1, if it is pure and the link of any face with cardinality at least t is Cohen-Macaulay. This generalizes several concepts on simplicial complexes such as Cohen-Macaualyness, Buchsbaum property, S_r condition of Serre, and locally Cohen-Macaulayness. Most results on the simplicial complexes with aforementioned properties naturally extend to the case of Cohen-Macaulayness in codimension t. In particular, the Eagon-Reiner theorem, the local behavior, and the homological vanishing properties are suitably retained. Furthermore, characterizations of certain families of Cohen-Macaulay simplicial complexes carry over characterizations of these families of simplicial complexes which are Cohen-Macaulay in codimension t. This talk is based on recent joint works with H. Haghighi, S. A. S. Fakhari and S. Yassemi. 1
08 Gen 2018
seminario di algebra e geometria
COHEN-MACAULAY SIMPLICIAL COMPLEXES IN ARBITRARY CODIMENSION
RAHIM ZAARE-NAHANDI (UNIVERSITY OF TEHRAN)
A simplicial complex of dimension d - 1 is said to be Cohen-Macaulay in codimension t, 0 <= t <=d -1, if it is pure and the link of any face with cardinality at least t is Cohen-Macaulay. This generalizes several concepts on simplicial complexes such as Cohen-Macaualyness, Buchsbaum property, S_r condition of Serre, and locally Cohen-Macaulayness. Most results on the simplicial complexes with aforementioned properties naturally extend to the case of Cohen-Macaulayness in codimension t. In particular, the Eagon-Reiner theorem, the local behavior, and the homological vanishing properties are suitably retained. Furthermore, characterizations of certain families of Cohen-Macaulay simplicial complexes carry over characterizations of these families of simplicial complexes which are Cohen-Macaulay in codimension t. This talk is based on recent joint works with H. Haghighi, S. A. S. Fakhari and S. Yassemi. 1