Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 11-01-2021 al 17-01-2021
Martedì 12 gennaio 2021
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=KIPGUg9VS-w, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
Serie di seminari IAC "AIM: Artificial Intelligence and Mathematics, fundamentals and beyond"
Pierluigi Contucci (Dipartimento di Matematica, Università di Bologna)
Matematica e apprendimento automatico, l'approccio meccanico statistico
Il machine learning sta avendo un impatto nella società paragonabile solo a quello dei motori durante la rivoluzione industriale. Oggi, come allora, la tecnologia precede la scienza e le chiede concetti unificanti e strumenti di comprensione come quelli della matematica con il suo approccio rigoroso e il suo apporto di idee, metodi e modelli. Il seminario intende fornire una prospettiva sull'uso di una classe di tali strumenti, quelli della meccanica statistica dei sistemi disordinati, che si stanno rivelando utili allo scopo.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 13 gennaio 2021
Ore 14:00, Seminario telematico via Google Meet all'URL http://meet.google.com/jjt-toji-skw, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Karin Baur (University of Leeds)
Cluster structures for Grassmannians
The coordinate ring of the Grassmannian has the structure of a cluster algebra. On the other side, the category of maximal CM modules over a certain infinite dimensional algebra Is a cluster category associated to this cluster algebra structure. We study this category, in particular in the tame cases. We also show how to associate frieze patterns to these cluster structures.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it
Giovedì 14 gennaio 2021
Ore 14:00, Seminario online su questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Matteo Muratori (Politecnico di Milano)
Nonlinear diffusion equations on noncompact manifolds and relations with stochastic completeness
We prove that the mass conservation property for the heat flow on a complete, connected, noncompact Riemannian manifold \(M\), namely stochastic completeness, is equivalent to the uniqueness of nonnegative bounded solutions for a certain class of nonlinear evolution equations. Such a connection was well known in the pure linear case only, i.e. for the heat equation itself. Here we consider equations of the type of \(u_t=\Delta(\phi(u))\), where \(\phi\) is any nonnegative, concave, increasing function, \(C^1\) away from the origin and satisfying \( \phi(0)=0 \). We provide optimal criteria for uniqueness/nonuniqueness of nonnegative, bounded (distributional) solutions taking general nonnegative, bounded initial data \(u_0\). In particular our results apply to the fast diffusion equation \(u_t=\Delta(u^m)\) (where \(m \in (0,1)\)), and they show that there is a large class of manifolds in which uniqueness actually fails. This is in sharp contrast, for instance, with the Euclidean case, where existence and uniqueness hold for merely \(L^1_{loc}\) initial data thanks to the theory developed by M.A. Herrero and M. Pierre in the '80s. We will also address existence/nonexistence of nonnegative, nontrivial, bounded solutions to a strictly related nonlinear elliptic equation and, if time allows, some work in progress devoted to removing the concavity assumption.
The talk is based on joint projects with G. Grillo, K. Ishige and F. Punzo.
Note: This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Giovedì 14 gennaio 2021
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)
David Stolnicki (Università di Roma Sapienza)
On a class of fully nonlinear elliptic equations in dimension two
In joint work with F. Pacella, we study the existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci's extremal operators in dimension two. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover for the (negative) Pucci P^- operator, we show the existence of a critical exponent and give bounds for it.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 14 gennaio 2021
Ore 16:00, On line Seminar , Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Andrea Venturelli (Université d'Avignon (France))
Hyperbolic motion in the Newtonian N-body problem with arbitrary limit shape
We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of a global viscosity solutions for the Hamilton-Jacobi equation H(x,du(x))=h. Our hyperbolic motion is in fact a calibrating curve of the viscosity solution. The presented results can also be viewed as a new application of Marchal’s theorem, whose main use in recent literature has been to prove the existence of periodic orbits. Joint work with Ezequiel Maderna. 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
Venerdì 15 gennaio 2021
Ore 15:00, modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1,
Seminario di Logica e Informatica Teorica
Federico Olimpieri (Università Roma Tre, Aix-Marseille Université)
Intersection Type Distributors
Building on previous works, we present a general method to define proof relevant intersection type semantics for pure lambda calculus. We argue that the bicategory of distributors is an appropriate categorical framework for this kind of semantics. We first introduce a class of 2-monads whose algebras are monoidal categories modelling resource management, following Marsden-Zwardt's approach. We show how these monadic constructions determine Kleisli bicategories over the bicategory of distributors and we give a sufficient condition for cartesian closedness. We define a family of non-extensional models for pure lambda calculus. We then prove that the interpretation of lambda terms induced by these models can be concretely described via intersection type systems. The intersection constructor corresponds to the particular tensor product given by the considered free monadic construction.
Per partecipare al seminario con Teams cliccare sul seguente Link
Venerdì 15 gennaio 2021
Ore 16:00, Il seminario sarà tenuto in modalità telematica, Link per partecipare: https://uniroma1.zoom.us/meeting/register/tZwtcOGqqzkpE9yen93NMtuUttv031ZmB9lt
Seminario per insegnanti (PLS)
Nicoletta Lanciano (Sapienza Università di Roma)
Geometria e astronomia: storia della misura e osservazione
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.
Per informazioni, rivolgersi all'indirizzo di posta elettronica
seminari@mat.uniroma1.it.
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