Bollettino settimanale
Settimana 02/05/2022 - 06/05/2022
Seminari
U.M.I. GROUP P.R.I.S.M.A.
PROBABILITY IN STATISTICS MATHEMATICS AND APPLICATIONS SEMINAR
Date: Monday may 2nd, 2022
Schedule: 16:00 Rome Time
Where: On-line Webinar
Speaker: LAURA SACERDOTE
Title: " nput-output consistency in Integrate and Fire neuronal networks"
Abstract: Models of neurons aim to describe the information transmission within a
neural network. Some models are mathematically tractable with the introduction of strong simplifications, ignoring the involved biophysicalfeatures of the single units. Others are very faithful to reality at the price of very complex mathematical descriptions. Models are then used to
describe networks, often through simulations. The appearance of particular patterns in the trains of spikes is then used to compare with observed data or to switch from microscopic to macroscopic analysis. In this framework, it is essential to guarantee the reliability of the output
of the model and often scientists compare the output of the models with real data. However, when the models are used to reproduce networks the output of some neurons becomes the input of a successive layer of neurons. This fact opens a problem of consistency between input and output of layers of neurons. To the best of our knowledge, this problem has not yet been deeply investigated. Here, we consider the simplest Stochastic Integrate and Fire model and we try to characterize the features of its input in such a way to re-obtain the same features in the output. In particular, we focus on the tail properties of ISIs distribution. Observed data suggest the presence of heavy tails for this distribution. Using the Stochastic Integrate and Fire paradigm for the neurons of the network we study how such features can be transmitted from the network. In this framework we introduce a particular class of multivariate distributions, i.e. the regularly varying distributions. We show that assuming that the input to a neuron is a regularly varying random vector and that successive ISIs of a neuron are asymptotically independent thenthe resulting output is a regularly varying random variable.
The talk is based on a joint work with Petr Lansky and Federico Polito.
Organizing Committee: Claudia Ceci (mail to) Domenico Marinucci (mail to)
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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
TOPOLOGY SEMINAR
Date: Wednesday May 4nd, 2022
Schedule: 15:00 Rome Time
Where: Room 20 Macroarea Scienze
Speaker: Eugenio Landi (Università Roma Tre)
Title: "Cobordismo, generi e coomologia equivariante "
Abstract: In un lavoro del 1985, Atiyah ricava il genere  di una varietà spin sfruttando il teorema di localizzazione equivariante. Si mostrerà come ottenere questo risultato e alcune generalizzazioni partendo dalle definizioni di base.
Organizing Committee: Paolo Salvatore (mail to)
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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
DIFFERENTIAL EQUATIONS SEMINAR
Date: Tuesday 3 May 2022
Schedule: 16:00 Rome Time
Where: Aula "Dal Passo" and Online (see the link below)
Speaker: Francesco Fidaleo (Università di Roma "Tor Vergata")
Title: "Spectral actions for q-particles and their asymptotic"
Abstract: For spectral actions made of the average number of particles and arising fromopen systems made of general free q-particles (including Bose, Fermi and classical ones corresponding to q=\pm 1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and massive particles, where the natural cut-off is 1/\beta=k_\beta T and 1/\sqrt{\beta}, respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium. We briefly discuss the appearance of condensation phenomena occurring for Bose-like q-particles, for which q\in(0,1], after passing to the continuum. We also compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).
Organizing Committee: Riccardo Molle (mail to) Alfonso Sorrentino (mail to)
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Università di Roma la Sapienza
Dipartimento di Matematica
MINI CONFERENCE IN ANALYSIS
Date: Mondey 4 - Tuesday 5 May 2022
Schedule: 14:30 Rome Time
Where: Aula Picone - Dipartimento di Matematica "Guido Castelnuovo"
Speaker:
Martino Bardi (University of Padova - Italy)
Olga Bernardi (University of Padova - Italy)
Fabio Camilli (Sapienza, University of Rome - Italy)
Piermarco Cannarsa (University of Rome Tor Vergata - Italy)
Annalisa Cesaroni (University of Padova - Italy)
Albert Fathi (Georgia Tech - USA)
Hitoshi Ishii (Waseda University - Japan)
Fabiana Leoni (Sapienza, University of Rome - Italy)
Olivier Ley (Institut de recherche de mathématiques de Rennes - France)
Marco Pozza (Sapienza, University of Rome - Italy)
Maxime Zavidovique (Universitè Pierre et Marie Curie - France)
Title: "The Hamilton-Jacobi equation in nonlinear PDEs, dynamics and optimal control: a celebration of Antonio Siconolfi's 70th birthday"
Abstract:
PROGRAM
Giovedì 5 maggio, 2022 (Aula Picone)
14:30-15:15 Albert Fathi: Some Facts about weak KAM
15:20- 16:05 Piermarco Cannarsa: Weak KAM theory for sub-Riemannian control systems
coffee break 16:05 -16:30
16:30- 17:15 Olga Bernardi
17:20- 18:05 Olivier Ley: A smooth convex function with spiraling gradient orbits
Venerdì 6 maggio, 2022
Mattina (Sala di Consiglio)
9-9:45 Martino Bardi: An Eikonal equation with vanishing Lagrangian arising in Global Optimization
9:50- 10:35 Fabio Camilli: A Mean Field Games approach to finite mixture models
coffee break 10:35 -11:00
11:00- 11:45 Annalisa Cesaroni: Long time behavior of fractional mean curvature flow
11:50- 12:35 Maxime Zavidovique: Degenerate discounted fist order Hamilton-Jacobi equations
Pomeriggio (Aula Picone)
14:30-15:15 Fabiana Leoni: New concentration phenomena for sign-changing radial solutions of fully nonlinear elliptic equations
15:20- 16:05 Marco Pozza: Lax–Oleinik formula on networks
coffee break 16:05 -16:30
16:30- 17:15 Hitoshi Ishii: Nonlinear Neumann problems for fully nonlinear elliptic PDEs on a quadrant
Organizing Committee: Isabeau Birindelli (mail to) Alfonso Sorrentino (mail to) Andrea Davini (mail to)
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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
PROBABILITY SEMINAR
Date: Tuesday 5 May 2022
Schedule: 16:00 Rome Time
Where: Room 1103 "F. De Blasi"
Speaker: Riccardo Maffucci (EPFL)
Title: "Distribution of nodal intersections for random waves"
Abstract: This is work is collaboration with Maurizia Rossi. Random waves are Gaussian Laplacian eigenfunctions on the 3D torus. We investigate the length of intersection between the zero (nodal) set, and a fixed surface. Expectation, and variance in a general scenario are prior work. In the generic setting we prove a CLT. We will discuss (smaller order) variance and (non-Gaussian) limiting distribution in the case of ’static’ surfaces (e.g. sphere). Under a certain assumption, there is asymptotic full correlation between intersection length and nodal area.
Organizing Committee: Michele Salvi (mail to) Domenico Marinucci (mail to)
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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
COMPLEX ANALYSIS SEMINAR
Date: Thursday, May 5 2022
Schedule: 17:00 - Rome Time
Where: Room 1101 " C. D'Antoni"
Speaker: Franz Forstnerič (Ljubljana University)
Title: "Oka domains in Euclidean spaces"
Abstract: We find surprisingly small Oka domains in complex Euclidean spaces of dimension n>1 at the very limit of what is possible.
Under mild geometric assumptions on a closed unbounded convex set E in C^n we show that the complement of E is an Oka domain. This holds in particular if E does not contain any affine real line.
Hence, there are Oka domains which are only slightly bigger than a halfspace, the latter being neither Oka nor hyperbolic. (Joint work with Erlend F. Wold.)
Organizing Committee: Leandro Arosio (mail to) Filippo Bracci (mail to)
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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
ALGEBRA AND REPRESENTATION THEORY SEMINAR
Date: Friday, May 6, 2022
Schedule: 14:30 Rome Time
Where: Room "Roberta Dal Passo"
Speaker: Peter FIEBIG ( Friedrich-Alexander-Universität Erlangen-Nürnberg)
Title: "Tilting modules and torsion phenomena"
Abstract: Given a root system and a prime number p we introduce a category X of “graded spaces with Lefschetz operators” over a ring A. Then we show that under a base change morphism from A to a field K this category specialises to representations of the hyperalgebra of a reductive group, if K is a field of positive characteristic, and of a quantum group at pl-th root of unity, if K is the pl-th cyclotomic field. In this category we then study torsion phenomena (over the ring A) and construct for any highest weight a family of universal objects with certain torsion vanishing condi-tions. By varying these conditions, we can interpolate between the Weyl modules (maximal torsion) and the tilting objects (no torsion). This construction might shed some light on the character generations philosophy of Lusztig and Lusztig-Williamson.
Organizing Committee: Fabio Gavarini (mail to) Martina Lanini (mail to)
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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
ALGEBRA AND REPRESENTATION THEORY SEMINAR
Date: Friday, May 6, 2022
Schedule: 16:00 Rome Time
Where: Room "Roberta Dal Passo"
Speaker: Francesco BRENTI Università degli Studi di Roma "Tor Vergata"
Title: " Graphs, stable permutations, and Cuntz algebra automorphisms"
Abstract: Stable permutations are a class of permutations that arises in the study of the automor-phism group of the Cuntz algebra. In this talk, after introducing the Cuntz algebra and surveying the main known results about stable permutations, I will present a characterization of stable permu-tations in terms of certain associated graphs. As a consequence of this characterization we prove a conjecture in [Advances in Math. 381 (2021) 107590], namely that almost all permutations are not stable, and we characterize explicitly stable 4 and 5-cycles. This is a joint work with Roberto Conti and Gleb Nenashev.
Organizing Committee: Fabio Gavarini (mail to) Martina Lanini (mail to)
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Eventi
Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
Corso di Dottorato
Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics
Period: 2022.11.04 - 2022.06.06
Schedule:
| Day | Period | Time |
|---|---|---|
| Monday | 11.04.2022 | 14:00 - 16:00 |
| Wednesday | 13.04.2022 | 14:00 - 16:00 |
| Monday | 20.04.2022 | 14:00 - 16:00 |
| Wednesday | 27.04.2022 | 14:00 - 16:00 |
| Monday | 02.05.2022 | 14:00 - 16:00 |
| Wednesday | 04.05.2022 | 14:00 - 16:00 |
| Monday | 09.05.2022 | 14:00 - 16:00 |
| Wednesday | 11.05.2022 | 14:00 - 16:00 |
| Monday | 16.05.2022 | 14:00 - 16:00 |
| Wednesday | 18.05.2022 | 14:00 - 16:00 |
| Monday | 23.05.2022 | 14:00 - 16:00 |
| Wednesday | 25.05.2022 | 14:00 - 16:00 |
| Monday | 03.05.2022 | 14:00 - 16:00 |
| Wednesday | 01.06.2022 | 14:00 - 16:00 |
| Monday | 06.06.2022 | 14:00 - 16:00 |
Where: Common Room
Organizing Committee: Benedetto Scoppola (Contatto E-Mail).
Speaker: Aldo Procacci (University Federal of the Minas Gerais, Belo Horizonte, Brasile)
Title: Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics
Speaker: Aldo Procacci (University Federal of the Minas Gerais, Belo Horizonte, Brasile)
Title: Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics
Abstract:
Course program:
Part 1. Continuous particles in the Grand Canonical Ensemble interacting via a pair potential
1. Conditions on the pair potential: stability and regularity
2. The infinite volume limit. Existence (the case of the finite range pair potential)
3. Properties of the pressure. Continuity.
4. The Mayer series
5. The combinatorial problem
6. The Penrose tree graph identity: partition schemes.
7. Analyticity at low density/high temperature
- a) The hard sphere gas (via the original Penrose partition scheme)
b) gas of particles interacting via a stable and regular pair potential (via the Kruskal algorithm partition scheme)
Part 2. Discrete systems
1. The abstract polymer gas
2. Convergence of the cluster expansion
3. Convergence criteria: Kotecký-Preiss; Dobrushin; Fernández-Procacci.
4. Elementary examples.
5. Gas of non-overlapping subsets
6. Applications: spin systems at high temperature
7. Ising model at low temperature.
8. Antiferromagnetic Potts model at zero temperature on a graph G (complex zeros of the chromatic polynomial of G).
Part 3. The Connection with the probabilistic method in combinatorics
1. A powerful tool in combinatorics: The Lovász Local Lemma
2. Shearer criterion.
3. Scott-Sokal formulation of the Shearer Criterion via the abstract polymer gas.
4. The cluster expansion Local lemma
5. Example: colorings of a graph.
6. The Moser-Tardos algorithmic version of the Lovász Local Lemma
7. Entropy-compression method.
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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
Corso di Dottorato
Introduction to rough paths
Period: 2022.05.04 - 2022.05.26
Schedule:
| Day | Period | Time |
|---|---|---|
| Wednesday | 2022.05.05 | 14:00 - 16:00 |
| Tuesday | 2022.05.11 | 14:00 - 16:00 |
| Wednesday | 2022.04.12 | 14:00 - 16:00 |
| Tuesday | 2022.05.18 | 14:00 - 16:00 |
| Wednesday | 2022.05.19 | 14:00 - 16:00 |
| Tuesday | 2022.05.23 | 14:00 - 16:00 |
| Wednesday | 2022.05.24 | 14:00 - 16:00 |
Where: Room 1201 Dal Passo
Organizing Committee: Lucia Caramellino (Contatto E-Mail).
Speaker: Vlad Bally (Université Gustave Eiffel, France)
Title: "Introduction to rough paths"
Speaker: Vlad Bally (Université Gustave Eiffel, France)
Title: "Introduction to rough paths"
Abstract: Rough path theory has been initiated in the last 90's by Terry Lyons in [1]. Then, in the last 20 years it has had a tremendous development, including the "regularity structures" theory of Hairer (we will not touch to this last topic in our course). And nowadays this is still an extremely active area of research. The aim of this theory is to construct a variant of the stochastic integral which is "pathwise". Moreover one solves Stochastic Differential Equations (SDEs) with the usual stochastic integral replaced by the "rough integral". This gives an application defined on the space of continuous functions C([0,T]) which, under the Wiener measure, produced the solution of the SDE. We stress that the classical theory of stochastic flows (due to Kunita, Bismut, and many others) produces a "strong solution" of the SDE, which is exactly such an application. But there is a crucial progress here: in the classical case, the flow produces a solution "almost surely" with an exception set depending on the coefficients of the SDE, whereas in the rough path theory the exception set is independent of the coefficients (in some sense it is universal). Moreover, a continuity property of the application, with respect to a specific norm (the "rough path norm") is proved. Nowadays there are many text books devoted to this subject. They are more or less difficult to read because of a rather heavy technical background. The aim of this introductory course is to give an elementary and simple approach to the main ideas in this theory. But of course, this is just a first step and a deep knowledge of the theory needs to read one of these books. I strongly recommend the beautiful book [2] of Friz and Hairer (which I will more or less follow).