Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 07-02-2022 al 13-02-2022

Lunedì 07 febbraio 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Alessandro Iacopetti (U. di Torino)
New regularity results for the prescribed mean curvature equation in the Lorentz-Minkowski space
In this talk we present some recent results concerning the existence and the regularity of weak solutions of the prescribed mean curvature equation in the Lorentz-Minkowski space (for spacelike hypersurfaces), when the mean curvature is in \(L^p\). In the first part of the talk we will show a new gradient estimate for entire smooth solutions of the prescribed mean curvature equation. Then we will prove that, if \(p>N\), then the unique minimizer of the Born-Infeld energy, which is a priori only Lipschitz continuous, is actually a strictly spacelike weak solution of the equation and it is of class \(W^{2,p}_{loc}\). Finally we will discuss some open problems. These results are collected in a series of joint works with Prof. D. Bonheure (Université Libre de Bruxelles).


Martedì 08 febbraio 2022
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' di Roma Tor Vergata
Seminario di Geometria
Paolo Stellari (Universita' di Milano)
Stability conditions in the trivial canonical bundle case: Hilbert schemes of points
The construction of stability conditions on the bounded derived category of coherent sheaves on smooth projective varieties is notoriously a difficult problem, especially when the canonical bundle is trivial. In this talk, I will review some results and techniques related to the latter setting. I will specifically concentrate on the case of Hilbert scheme of points on K3 surfaces and (as a work in progress) on generic abelian varieties of any dimension. This is joint work in progress with C. Li, E. Macri' and X. Zhao.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it


Martedì 08 febbraio 2022
Ore 16:00, Aula "Dal Passo" and online seminar on this link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Azahara DelaTorre (Università di Roma "La Sapienza")
The fractional Yamabe problem with singularities
The so called Yamabe problem in Conformal Geometry consists in finding a metric conformal to a given one and which has constant scalar curvature. From the analytic point of view, this problem becomes a semilinear elliptic PDE with critical (for the Sobolev embedding) power non-linearity. If we study the problem in the Euclidean space, allowing the presence of nonzero-dimensional singularities can be transformed into reducing the non-linearity to a Sobolev-subcritical power. A quite recent notion of non-local curvature gives rise to a parallel study which weakens the geometric assumptions giving rise to a non-local semilinear elliptic PDE. In this talk, we will focus on metrics which are singular along nonzero-dimensional singularities. In collaboration with Ao, Chan, Fontelos, González and Wei, we covered the construction of solutions which are singular along (zero and positive dimensional) smooth submanifolds in this fractional setting. This was done through the development of new methods coming from conformal geometry and Scattering theory for the study of non-local ODEs. Due to the limitations of the techniques we used, the particular case of ``maximal’’ dimension for the singularity was not covered. In a recent work, in collaboration with H. Chan, we cover this specific dimension constructing and studying singular solutions of critical dimension.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it


Mercoledì 09 febbraio 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Ruggero Bandiera (Sapienza Università di Roma)
Mappe di semiregolarità e teoria di Chern-Simons
Dopo alcuni richiami sull'approccio alla teoria delle deformazioni tramite DG algebre di Lie (o più in generale algebre L-infinito), ci concentreremo sullo studio delle deformazioni di un fascio coerente \(F\) su una varietà proiettiva complessa \(X\): queste sono controllate dall'algebra degli endomorfismi derivati di \(F\), ed in particolare le ostruzioni alle deformazioni di \(F\) vivono nello spazio \(\text{Ext}^2(F,F)\). In questa situazione, Buchweitz e Flenner (arXiv:math/9912245) introducono una famiglia di applicazioni lineari, dette mappe di semiregolarità, dallo spazio delle ostruzioni \(\text{Ext}^2(F,F)\) a valori nella coomologia di \(X\), e dimostrano che queste annullano una classe particolare di ostruzioni, dette ostruzioni curvilinee. Nell'ultima parte del seminario esporremo alcuni recenti risultati ottenuti in collaborazione con M. Manetti ed E. Lepri (arXiv:2111.12985). Usando la teoria di Chern-Simons, costruiremo modelli L-infinito delle mappe di semiregolarità di Buchweitz-Flenner, mostrando che queste sono indotte da morfismi di teorie delle deformazioni con target non ostruito, ed in particolare annullano tutte le ostruzioni alle deformazioni di \(F\) (non solo quelle curvilinee).
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it


Mercoledì 09 febbraio 2022
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=Xz8oqUSmMZ8, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Online Seminars on Artificial Intelligence and Mathematics 2022 https://www.aim.iac.cnr.it/home
Carola-Bibiane Schönlieb (Department of Applied Mathematics and Theoretical Physics (DAMTP) - University of Cambridge)
AI and mathematical imaging - the what, why and how
Mathematical imaging is a topic that touches upon several areas of mathematics, engineering and computer science, including functional and non-smooth analysis, the theory and numerical analysis of partial differential equations, harmonic, stochastic and statistical analysis, optimisation and machine learning. In this talk we will learn about some of these mathematical problems, about variational models for image analysis and their connection to partial differential equations and about a new paradigm in mathematical imaging using deep neural networks. The talk is furnished with applications to art restoration, forest conservation and cancer research.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it


Mercoledì 09 febbraio 2022
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Alessia Nota (Università dell'Aquila)
Homoenergetic solutions of the Boltzmann equation
In this talk I will consider a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which were introduced by Galkin and Truesdell in the 1960s. These are a particular type of non-equilibrium solutions of the Boltzmann equation and they are useful to describe the dynamics of Boltzmann gases under shear, expansion or compression. Due to the fact that these solutions describe far-from-equilibrium phenomena their long-time asymptotics cannot always be described by Maxwellian distributions. For several collision kernels the asymptotics of homoenergetic solutions is given by particle distributions which do not satisfy the detailed balance condition. I will discuss different possible long-time asymptotics of homoenergetic solutions of the Boltzmann equation, as well as some conjectures and open problems in this direction. These are joint works with A.V.Bobylev, R.D.James and J.J.L.Velàzquez.


Giovedì 10 febbraio 2022
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n) Problemi Differenziali Non Lineari
Antonio Siconolfi (Sapienza Università di Roma)
Hamilton-Jacobi equations and optimal transport
We relate a time-dependent Hamilton-Jacobi equation posed on the n-dimensional torus to an optimal transport problem. We provide a version of Kantorovich duality theorem and of Brenier-Benamou formula adapted to the framework.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it


Giovedì 10 febbraio 2022
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Chi è interessato a partecipare può rivolgersi ad Annalisa Cusi
Seminari di Ricerca in Didattica e Storia della Matematica
Maria Anna Raspanti (Sapienza Università di Roma)
Giovanni Virginio Schiaparelli e le trasformazioni geometriche delle figure piane

Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it


Venerdì 11 febbraio 2022
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Domenico Fiorenza (Sapienza Università di Roma)
Brackets and products from centres in extension categories
Building on Retakh's approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras both from splicing extensions (leading to the cup product) and from a suitable loop in the categories of extensions (leading to the Lie bracket). We show how Schwede's construction admits a vast generalisation to general monoidal categories with coefficients of the Ext groups taken in (weak) left and right monoidal (or Drinfel'd) centres. In case of the category of left modules over bialgebroids and coefficients given by commuting pairs of braided (co)commutative (co)monoids in these categorical centres, we provide an explicit description of the algebraic structure obtained this way, and a complete proof that this leads to a Gerstenhaber algebra is then obtained from an operadic approach. This, in particular, considerably generalises the classical construction given by Gerstenhaber himself. Conjecturally, the algebraic structure we describe should produce a Gerstenhaber algebra for an arbitrary monoidal category enriched over abelian groups, but even the bilinearity of the cup product and of the Lie-type bracket defined by the abstract construction in terms of extension categories remain elusive in this general setting. Joint work with Niels Kowalzig; arXiv:2112.11552.
Link per seguire in streaming


Venerdì 11 febbraio 2022
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Corrado De Concini (Sapienza Università di Roma & Accademia delle Scienze)
Paving Springer Fibers. The E7 case
In the paper De Concini, C.; Lusztig, G.; Procesi, C. Homology of the zero-set of a nilpotent vector field on a flag manifold. J. Amer. Math. Soc. 1 (1988), no. 1, 15-34, it was proven the so called Springer fiber \(\mathcal{B}_n\) for any nilpotent n element in a complex simple Lie algebra \(\mathfrak{g}\) has homological properties that suggest that \(\mathcal{B}_n\) should have a paving by affine spaces. This last statement was proved to hold in the case in which \(\mathfrak{g}\) is classical but remained open for exceptional groups in types E7 and E8. In a joint project with Maffei we are trying to fill this gap. At this point our efforts has been successful in type E7 and "almost" in type E8 were one is reduced to show it only in one case. The goal of the talk is to survey the problem and give an idea on how to show our new results.
Link per seguire in streaming


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.
Coloro che desiderano ricevere questo notiziario via e-mail sono pregati di comunicare il proprio indirizzo di posta elettronica a seminari@mat.uniroma1.it.

© Università degli Studi di Roma "La Sapienza" - Piazzale Aldo Moro 5, 00185 Roma