Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 13-01-2020 al 19-01-2020
Lunedì 13 gennaio 2020
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Maria Gordina (University of Connecticut)
Ergodicity for Langevin dynamics with singular potentials
We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus. In contrast to previous results for such systems, our results imply geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on join work with F.Baudoin and D.Herzog.
Martedì 14 gennaio 2020
Ore 10:10, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario dei Giovani Ricercatori
Alfie Mimun Hlafo (Sapienza)
Percolation theory and applications
In physics the term "percolation" refers to the filtering of fluids through porous media. Many models for random graphs have been introduced to study this physical phenomenon. The main question concerns the "size" of the biggest connected component. In particular many models exhibit a phase transition when studying the probability of the existence of an unbounded connected component. In this talk we will explain some models in this field and study relevant quantities in different regimes. Moreover we will show some applications.
Martedì 14 gennaio 2020
Ore 11:35, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario dei Giovani Ricercatori
Mattia Coloma (Tor Vergata)
The Hirezebruch-Riemann-Roch theorem in the fancy language of Spectra
The category of spectra indubitably is the best of possible worlds for cohomology theories. For instance in spectra one can start with a few basic morphisms, be confident that every natural diagram built from them will commute, and end up with a proof of the Hirzebruch-Riemann-Roch theorem. As in every good story we'll have a deus ex machina: Atiyah's identification of the Spanier-Whitehead dual of a manifold with the Thom spectrum of minus its tangent bundle. I will try to gently introduce all of this tools assuming basic notions of topology, geometry and algebra. Based on joint work with Domenico Fiorenza and Eugenio Landi.
Martedì 14 gennaio 2020
Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Corso di dottorato
Aldo Procacci (Università di Belo Horizonte)
A connection between the Lovász local Lemma in combinatorics and the abstract polymer system in statistical mechanics - prima lezione
Programma del corso - The Lovász Local Lemma (LLL) - Dependency graph of a family of events in a probability space. - Abstract polymer system (APS) setting in statistical mechanics and its fundamental problem solved via cluster expansion. Kotecky-Preiss Criterion, Dobrushin criterion and Fernández-Procacci criterion. - Connection between LLL e APS via the re-elaboration of the Shearer Theorem made by Scott and Sokal and new "cluster expansion" local lemma improving the LLL. 4) Moser Tardos algorithmic version of the LLL and Pegden improvement 5) Applications in combinatorics. Graph coloring problems. All'inizio della prima lezione saranno stabiliti giorni e orari delle successive lezioni.
Martedì 14 gennaio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza
seminario di Probabilità
Antonio Galves (Universidade de Sao Paulo)
Estimating the interaction graph of stochastic neural dynamics
We address the question of statistical model selection for a class of stochastic models of biological neural nets.Models in this class are systems of interacting chains with memory of variable length. Each chain describes the activity of a single neuron, indicating whether it spikes or not at a given time. The spiking probability of a given neuron depends on the time evolution of its presynaptic neurons since its last spike time. When a neuron spikes, its potential is reset to a resting level and postsynaptic current pulses are generated, modifying the membrane potential of all its postsynaptic neurons. The relationship between a neuron and its pre- and postsynaptic neurons defines an oriented graph, the interaction graph of the model. The goal is to estimate this graph based on the observation of the spike activity of a finite set of neurons over a finite time. We provide explicit exponential upper bounds for the probabilities of under- and overestimating the interaction graph restricted to the observed set and obtain the strong consistency of the estimator. Our result does not require stationarity nor uniqueness of the invariant measure of the process. Joint work with A. Duarte, E. Locherbach and G. Ost.
Martedì 14 gennaio 2020
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni differenziali
Rafael Oswaldo Ruggiero (PUC Rio de Janeiro)
Time preserving expansive models for geodesic flows of compact surfaces without conjugate points and the uniqueness of the measure of maximal entropy
We show that the geodesic flow of a compact surface of genus greater than one without conjugate points and continuous Green bundles is time-preserving semi-conjugate to an expansive flow acting on a compact 3-dimensional manifold. As a by-product of this result we get a short proof of the uniqueness of the measure of maximal entropy of the geodesic flow, a result proved by Knieper-Climegnaga-Kwar and independently Leddrapier-Lima-Sarig, by completely different methods.
Martedì 14 gennaio 2020
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Luca Saluzzi (GSSI)
A Tree-Structure algorithm for optimal control problems via Dynamic Programming
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical approximation of viscosity solutions of those equations is typically based on a time discretization which is projected on a fixed space triangulation of the numerical domain. In this talk, we will discuss a new approach for finite horizon optimal control problems where we compute the value function on a tree structure built directly by the time discrete dynamics avoiding the use of a space triangulation to solve the HJB equation. This allows to drop the cost of the space interpolation and guarantees a perfect matching with the discrete dynamics. We will also provide error estimates for the algorithm if the dynamics is discretized with an Euler method. Furthermore, this approach has been extended to high-order schemes and we will show some examples of second order approximation schemes. Finally we will show the effectiveness of the method for the control of PDEs, considering the coupling of the method with the Proper Orthogonal Decomposition. This is a joint work with Maurizio Falcone and Alessandro Alla (PUC).
Mercoledì 15 gennaio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Jorge Vitorio Pereira (IMPA)
Miyaoka's algebraicity criterion and variations
I will review some old and new results/arguments on the algebraicity of leaves of foliations with "positive" tangent sheaf.
Giovedì 16 gennaio 2020
Ore 14:00, Aula 211 , Dipartimento di Matematica e Fisica Largo S. L. Murialdo, 1
Seminario di Geometria
Claudio Pedrini (Università di Genova)
The transcendental motive of a cubic fourfold
We introduce the transcendental motive t(X) of a complex cubic fourfold X in P5 and relate the existence of a K3 surface S, such that the (twisted) transcendental motive of S is isomorphic to t(X), with the conjectures about the rationality of X. We also show that the motive of the Fano variety F(X) and of the 8-dimensional hyperk alher variety Z, constructed by Ch. Lehn, M. Lehn, Ch. Sorger and D. van Straten, lie in the same subcategory of the Chow motives generated by t(X) and the Lefschetz motive L.
Giovedì 16 gennaio 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Francesca De Marchis (Sapienza Università di Roma)
Analisi asintotica, indice di Morse e conseguenze per una classe di problemi ellittici
In questo seminario presenterò alcuni risultati relativi a una classe di problemi ellittici semilineari. In particolare mi concentrerò sull'analisi asintotica di soluzioni (quando un parametro tende ad una soglia critica) e sull'indice di Morse delle soluzioni, mostrando poi come dalla conoscenza di tale indice si possano ottenere in alcuni casi risultati di unicità e in altri casi risultati di molteplicità.
Giovedì 16 gennaio 2020
Ore 15:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di ricerca in Didattica della Matematica
Claudio Bernardi (Sapienza Università di Roma)
Sulla dimostrazione
Venerdì 17 gennaio 2020
Ore 12:00, Sala Consiglio, Dipartimento di Matematica, Sapienza
Seminario di Geometria
Jonathan Rosenberg (University of Maryland)
The Riemann-Roch Theorem for Noncommutative Complex Tori
We discuss analogues of 3 important classical theorems about complex tori, C^n/L, L a lattice in C^n, for noncommutative complex tori (which we will define). The 3 basic theorems are the Riemann-Roch Theorem, the Hodge Theorem, and the characterization of when a complex torus is an abelian variety. This is joint work with V. Mathai of the University of Adelaide.
Venerdì 17 gennaio 2020
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di "Tor Vergata"
Algebra and Representation Theory Seminar
Kenji Iohara (Université de Lyon 1)
On elliptic root systems
Elliptic root systems are introduced in 1985 by K. Saito having simply elliptic singularities in mind. In this talk, the state of art around elliptic root systems will be explained.
Venerdì 17 gennaio 2020
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per docenti (PLS)
Riccardo Faccini (Sapienza Università di Roma)
Lab2Go e Share Science: strumenti per l'insegnamento
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