Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 11-04-2022 al 17-04-2022
Lunedì 11 aprile 2022
Ore 14:30, Aula II, Dipartimento di Matematica, Sapienza Università di Roma
Baby A&G Seminar
Enrico Fatighenti (Sapienza Università di Roma)
Alla ricerca delle rette. Che fare?
Una retta è a priori un oggetto tra i più semplici e innocui in geometria. Se però consideriamo l'insieme delle rette contenute in un certo oggetto, questo ha spesso una struttura interessante. L'esempio base è dato da uno spazio vettoriale V, il cui insieme delle rette passanti per l'origine è esattamente lo spazio proiettivo P(V). In questo seminario ci occuperemo di analizzare lo spazio delle rette in alcuni oggetti geometrici ("varietà"), e scopriremo come questi ammettano una struttura estremamente regolare e interessante. Risponderemo infine alla seguente (annosa) questione: cosa succederebbe se svegliassimo un geometra algebrico nel cuore della notte urlando "27"?
Lunedì 11 aprile 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Flavia Smarrazzo (U. Campo Biomedico-Roma)
Radon measure-valued solutions for a class of evolution equations with degenerate coerciveness and measure data
Initial-boundary value problems for nonlinear parabolic equations ut = ∆ɸ having Radon measures as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. More recently, solutions have been defined and investigated, which for positive times take values in the space of finite Radon measures. Such solutions are often called Radon measure-valued, to distinguish them from function-valued solutions. In general, whether the solution of the problem is a function for some time t>0 can be regarded as a M-L1 regularizing effect. The aim of this talk is to address well-posedness and regularity results, depending on whether or not the initial data charge sets of suitable capacity (determined by the growth order of ɸ), and on suitable compatibility conditions, describing the behaviour of the singular part of solutions. The diffusion function ɸ is only assumed to be continuous, nondecreasing and at most powerlike: no assumptions about existence or estimates from below of the diffusivity ɸ’ are made (except for some regularization results). This lack of regularity and strong coercivity, along with the possible occurrence of infinitely many nondegenerate intervals where ɸ is constant, requires using more refined compactness arguments and Young measure techniques in the proof of existence, which is in turn obtained by a suitable approximation procedure of the initial measure. The possible occurrence or lack of instantaneous M-L1 regularizing effects, as well as partial uniqueness results, will also be discussed.
Martedì 12 aprile 2022
Ore 16:00, Aula Dal Passo (and Streaming via MS Teams), Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Valerio Assenza (Heidelberg University)
Magnetic Curvature and Closed Magnetic Geodesic
A Magnetic System describes the motion of a charged particle moving on a Riemannian Manifold under the influence of a magnetic field. Trajectories for this dynamics are called Magnetic Geodesics and one of the main tasks in the theory is to investigate the existence of Magnetic Geodesic which are closed. In general this depends on the magnetic system taken into account and on the topology of the base space. Inspired by the work of Bahri and Taimanov, I will introduce the notion of Magnetic Curvature which is a perturbation of the standard Riemannian curvature due to the magnetic interaction. We will see that Closed Magnetic Geodesic exist when the Magnetic Curvature is positive, which happens , for instance, when the magnetic field is sufficiently strong. 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
Mercoledì 13 aprile 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Diego Corro (Universität zu Köln)
Yamabe type problems and singular Riemannian foliations
The Yamabe problem is a classical problem about how to find Riemannian metrics of constant scalar curvature. This problem can be written as a PDE with unique positive solutions. On the other hand, the problem of finding general solutions to the Yamabe PDE turns out to be a very complicated one.
Given that group actions by isometries and geometric projections are particular types of singular Riemannian foliations, in this talk we consider singular Riemannian foliations as a form of symmetry. Using this notion of symmetry together with techniques of calculus of variations, we show how to find an infinite number of general solutions to the Yamabe problem, which are constant along the leaves of the foliation.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it
Mercoledì 13 aprile 2022
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Alexander Lytchak (Universität zu Köln)
Four dimensional Hadamard manifolds are Euclidean
I will give an overview about topology of CAT(0) manifolds and will explain why in four dimensions every such manifold is homeomorphic to the Euclidean space. This is a joint work with Nagano-Stadler.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.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.
Per informazioni, rivolgersi all'indirizzo di posta elettronica
seminari@mat.uniroma1.it.
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