Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 24-05-2021 al 30-05-2021
Martedì 25 maggio 2021
Ore 14:15, https://zoom.us/j/94814686524?pwd=MHRIR2hIZ1VjRFpWTS82WlJPd2RWdz09, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Francisco J.Silva (Università di Limoges (Francia))
Mean field games, second lesson
In this lesson we will discuss some existence and uniqueness results for the standard time-dependent second order MFG system with non-local couplings. Next, we introduce the corresponding ergodic problem and discuss the relation between these two systems.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Mercoledì 26 maggio 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
Simon Riche (Université Clermont Auvergne)
Perverse sheaves on affine flag varieties, geometry of the dual group, and representations
The description of regular blocks of the category O of a complex semisimple Lie algebra in terms of perverse sheaves on a flag variety has been a crucial tool for its study, and in particular for the proof of the Kazhdan-Lusztig character formula. This description has a conjectural analogue for representations of reductive groups over fields of positive characteristic, as predicted by Finkelberg-Mirkovic, which involves a category of perverse sheaves on the affine Grassmannian of the Langlands dual group, with coefficients in a field of positive characteristic. In this talk I will present a work in progress with Bezrukavnikov which we expect will lead to a proof of this conjecture. As a step towards this goal, we obtain a description of tilting perverse sheaves on the affine flag variety reminiscent of the corresponding result for usual flag varieties due to Soergel.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it
Mercoledì 26 maggio 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Guido Gentile (Università di Roma Tre)
Pseudo-synchronous solutions for dissipative non-autonomous systems
We consider a class of systems on the one-dimensional torus, subject to a periodic perturbation and in the presence of dissipation, and show that, however small the dissipation, if the perturbation is a trigonometric polynomial in the angles and the unperturbed frequencies satisfy a non-resonance condition of finite order, depending on the size of the dissipation, then a quasi-periodic solution persists. A physically relevant case, where the result applies, is the spin-orbit model, which describes the rotation of a satellite around its own axis, while revolving on a Keplerian orbit around a planet, in the case in which the dissipation is taken into account through the MacDonald torque.
Mercoledì 26 maggio 2021
Ore 16:00, Online seminar, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Algebre di Operatori
Fabio Cipriani (Politecnico Milano)
Densities and their measurability in NCG
The aim of the talk is to provide conditions ensuring Connes' measurability of the canonical, \((1,\infty)\)-summable, spectral weight \(\rho(D)\), we associate to any self-adjoint operator \(D\) with discrete spectrum and of its associated state \(\phi_D(T):={\rm Tr\,}_\omega (T\rho(D))\). The framework allows to discuss measurability for discrete groups with sub-exponential growth and \(\theta\)-summable spectral triples. Examples also include 1. the volume density of Euclidean domains of infinite volume 2. densities on the C\(^*\)-algebra of pseudo-differential operators of 0-order on a compact Riemannian manifold 3. densities on Toeplitz extensions. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. Link
Per informazioni, rivolgersi a: v.morinelli@gmail.com
Giovedì 27 maggio 2021
Ore 14:00, Streaming via MS Teams (see link in the abstract), Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Costante Bellettini (University College London (UK))
Existence of hypersurfaces with prescribed-mean-curvature
Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz non-negative (or non-positive) function on N. We prove that there exists a closed hypersurface M whose mean curvature attains the values prescribed by g (joint work with Neshan Wickramasekera, Cambridge). Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C^2 immersed and two-sided (it admits a global unit normal); the scalar mean curvature at x is g(x) with respect to a global choice of unit normal. More precisely, the immersion is a quasi-embedding, namely the only non-embedded points are caused by tangential self-intersections: around such a non-embedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant, in which the above result gives a CMC (constant-mean-curvature) hypersurface for any prescribed value of the mean curvature. The construction of M is carried out largely by means of PDE principles: (i) a minmax for an Allen--Cahn (or Modica-Mortola) energy, involving a parameter that, when sent to 0, leads to an interface from which the desired PMC hypersurface is extracted; (ii) quasi-linear elliptic PDE and geometric-measure-theory arguments, to obtain regularity conclusions for said interface; (iii) parabolic semi-linear PDE (together with specific features of the Allen-Cahn framework), to tackle cancellation phenomena that can happen when sending to 0 the Allen-Cahn parameter. Note: This talk is supported by the MIUR Department of Excellence Project MATH@TOV Link for the streaming
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Giovedì 27 maggio 2021
Ore 14:30, Canale Youtube Cnr-Iac https://www.youtube.com/watch?v=UHRZ3exG9Jc, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
Seminari Generali IAC 2021
Christine Nardini (Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche)
Revisiting inflammation towards non-pharmacological therapies
Non-Communicable diseases (NCDs including cancers, autoimmune and chronic diseases) have represented a silent pandemic long before the dramatic rise of covid-19. NCDs are well known to be characterized by chronic inflammation and altered wound healing (i.e. the biological process that enables the return to the physiological state after an injury of mechanical, electrical, or optical nature), yet medical approaches leverage mostly on the former (anti-inflammatory therapies). Nevertheless, electrical, mechanical, and optical stimuli are occasionally used to treat NCDs, with however no clear rationale nor protocols. Investigation of the tight interaction of the role of wound healing in a broader inflammatory perspective may offer cost-effective means to prevent the progression of NCDs. I will present hypotheses, preliminary results, and perspectives of this intriguingly neglected therapeutic option.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Giovedì 27 maggio 2021
Ore 14:30, Il Seminario sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Geometria
Gavril Farkas (Humboldt-Universität)
The Kodaira dimension of the moduli space of curves: recent progress on a century-old problem
The problem of determining the birational nature of the moduli space of curves of genus g has received constant attention in the last century and inspired a lot of development in moduli theory. I will discuss progress achieved in the last 12 months. In particular, making essential of tropical methods it has been showed that both moduli spaces of curves of genus 22 and 23 are of general type (joint with D. Jensen and S. Payne).
Per partecipare al seminario cliccare sul seguente Link
Giovedì 27 maggio 2021
Ore 14:30, Sala di Consiglio - https://meet.google.com/ads-dekx-bgm, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)
Biagio Cassano (Università di Bari)
Sharp exponential decay for solutions to the Dirac equation
We determine the largest rate of exponential decay at infinity for non-trivial solutions to the stationary Dirac equation in presence of a (possibly non-Hermitian) matrix-valued perturbation V such that |V(x)| ~ |x|^{−ε} at infinity, for −∞ < ε < 1. Also, we show that our results are sharp for n = 2, 3, providing explicit examples of solutions that have the prescribed decay, in presence of a potential with the related behaviour at infinity. In this sense, our work is a result of unique continuation from infinity for the Dirac operator. Finally, we discuss the connections of this problem with the analogous one for the Laplace equation, the so called Landis’ conjecture.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 28 maggio 2021
Ore 10:00, https://zoom.us/j/94253429830?pwd=TmhsUjBnUVUwWEd6MFlLbzE4ZXdOQT09, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Francisco J. Silva (Università di Limoges (Francia))
Mean field games, third lesson.
In this lesson we provide some existence and uniqueness results for some MFGs with local couplings which have a variational structure. The proofs here rely on classical techniques from convex analysis. The latter are also useful in order to solve numerically the finite-difference scheme introduced by Achdou and Capuzzo-Dolcetta in 2010.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Venerdì 28 maggio 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Alessio Cipriani (Università di Roma "Tor Vergata")
Perverse Sheaves, Finite Dimensional Algebras and Quivers
In this talk I will introduce the category of perverse sheaves on a topologically stratified space X and give some examples. Then, I will show that when X has finitely many strata, each with finite fundamental group, such category is equivalent to a category of modules over a finite dimensional algebra A. Finally, I will discuss some algebraic approaches one can use in order to describe the algebra A.
This talk is based on joint work with Jon Woolf.
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