Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 31-05-2021 al 06-06-2021
Martedì 01 giugno 2021
Ore 14:30, Canale Youtube Cnr-Iac https://www.youtube.com/watch?v=IqhkVs1s1ZI, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
AIM: Artificial Intelligence and Mathematics, fundamentals and beyond
Daniele Peri (Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche)
Ottimizzazione + Intelligenza Artificiale & Machine Learning = ?
Il settore dell'ottimizzazione rappresenta il terreno di incontro diverse discipline. Anche per questa ragione, tecniche e metodologie che provengono da settori diversi trovano applicazione nel campo dell'ottimizzazione e viceversa, a volte senza una vera consapevolezza della loro equivalenza. Osserveremo quindi come tecniche sviluppate per risolvere alcune classi di problemi dell'ottimizzazione continua vincolata rappresentino di fatto un punto di contatto con il mondo dell'Intelligenza Artificiale e del Machine Learning. E viceversa.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Giovedì 03 giugno 2021
Ore 14:00, Streaming via MS Teams, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Francesco Carlotta Chittaro (Université de Toulon (France))
Hamiltonian approach to sufficient optimality conditions
The celebrated Pontryagin Maximum Principle (PMP) provides a (first order) necessary condition for the optimality of trajectories of optimal control problems. In most cases, however, a trajectory satisfying PMP is not optimal. For these reasons, additional optimality conditions are required. In this context, Hamiltonian methods are quite effective in establishing sufficient optimality conditions. In this talk, after a brief review of the main ideas of the general method, we will focus on optimal control problems associated with control-affine dynamics and costs of the form \( \int_0^T |u(t)| |\varphi( X(t))| dt \). Costs of these form are very common in problems modeling neurobiology, mechanics and fuel-consumption. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 MS Teams Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Giovedì 03 giugno 2021
Ore 16:30, Online seminar, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Prof. Dr. Detlev Buchholz (Mathematisches Institut, Universitaet Goettingen)
Resolvent algebras and Bose-Einstein-condensation
The treatment of non-relativistic interacting bosonic systems, exhibiting condensation in the limit of large particle numbers, is commonly based on studies of single particle density matrices, determined from the microscopic equilibrium states. In order to exhibit more detailed properties of these states, such as correlations between observables, one needs an algebra that is stable under the underlying dynamics and remains meaningful in the limit. In the present talk it is shown that the resolvent algebra of canonical quantum systems provides such a framework. The popular mean field, dilute gas and Gross-Pitaevskii approximations of the interactions lead to C*-dynamical systems based on the resolvent algebra. This fact implies that the limits of equilibrium states are still in equilibrium, satisfying the KMS condition. Moreover, the resolvent algebra contains all observables needed to study the condensates and their thermal background. If time permits, these results are illustrated by examples. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. Link for the online seminar: Please write to v.morinelli@gmail.com (Vincenzo Morinelli) or ciolli@mat.uniroma2.it (Fabio Ciolli)
Per informazioni, rivolgersi a: v.morinelli@gmail.com
Venerdì 04 giugno 2021
Ore 10:00, https://zoom.us/j/95624873567?pwd=V2QyQk1YaGtxb3ZxYVluMll0K1kyZz09, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Francisco J. Silva (Università di Limoges (Francia))
Mean field games, fourth lesson
In this lesson we study first order MFGs. We will present a convergence result for Nash equlibria of the game with N players to a MFG equilibrium as N tends to infinity. Then we study the relation between the characterization of equilibrium in terms of the standard first order MFG system and the characterization in terms of a probability measure over optimal paths.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Venerdì 04 giugno 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Abel Lacabanne (UC Louvain)
An asymptotic cellular category for G(e,e,n)
Given a Coxeter group \(W\), one may consider its Hecke algebra, which is a deformation of the group algebra of \(W\). Kazhdan and Lusztig have constructed the celebrated Kazhdan--Lusztig basis, which has many interesting properties. This basis can be used to construct a partition of \(W\) into Kazhdan--Lusztig cells, a partition of the irreducible complex representations of \(W\) into families and also a partition of the "unipotent characters" of \(W\) into families. There exist categorical counterparts of these objects, and the goal of this talk is to explain a tentative towards a partial generalization for the complex reflection group \(G(e,e,n)\). First, I will describe the situation of a Coxeter group and then explain briefly what can be extended to (some) complex reflection groups. Finally, I will turn to an description of the asymptotic category, which is constructed from representations of quantum \(\mathfrak{sl} _n\) at a \(2e\)-th root of unity, and try to justify the term "asymptotic cellular category".
Venerdì 04 giugno 2021
Ore 16:00, Streaming via Zoom and Youtube channel , Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Matteo Tanzi (New York University (USA))
Random-like properties of chaotic forcing
We prove that skew systems with a sufficiently expanding base have “approximate” statistical properties similar to random ergodic Markov chains. For example, they exhibit approximate exponential decay of correlations, meaning that the exponential rate is observed modulo a controlled error. The fiber maps are only assumed to be Lipschitz regular and to depend on the base in a way that guarantees diffusive behaviour on the vertical component. The assumptions do not imply an hyperbolic picture and one cannot rely on the spectral properties of the transfer operators involved. The approximate nature of the result is the inevitable price one pays for having so mild assumptions on the dynamics on the vertical component. The error in the approximation is shown to go to zero when the expansion of the base tends to infinity. Note: The zoom link to the seminar will be posted on https://www.dinamici.org/dai-seminar/ and on https://mathseminars.org/seminar/DinAmicI. Moreover, it will be streamed live on youtube via the DinAmicI channel: https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente
mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana
interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
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seminari@mat.uniroma1.it.
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