Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 27-03-2023 al 02-04-2023
Lunedì 27 marzo 2023
Ore 11:00, aula "Roberta Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Corso di dottorato
Marco Trevisiol (Università di Roma “La Sapienza”)
Springer Correspondence
This course aims to present one of the first results in geometric representation theory: the Springer Correspondence. The goal of geometric representation theory is to study representations of certain algebraic structures (finite Weyl groups, in our case) via geometric methods. Springer’s result (generalised in several ways and still a central tool nowadays) achieves a construction of all representations of a finite Weyl group (e.g. the symmetric group) in terms of the cohomology of a certain variety. The striking point of Springer’s construction is that the Weyl group action he discovers is highly non trivial and hidden, since the Weyl group does not act on the variety itself. Some of the arguments we are going to address are: representation theory of the symmetric group via tableaux combinatorics; flag variety and Bruhat decomposition; nilpotent cone, the Springer resolution, Springer fibres; construction of the Weyl group action on the cohomology of the Springer sheaf. The discussion will be more or less detailed, depending on the participants’ background and interests.
Per informazioni, rivolgersi a: lanini@mat.uniroma2.it
Lunedì 27 marzo 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Carlo Sinestrari (Università di Roma "Tor Vergata")
Moto per curvatura a volume costante e disuguaglianze isoperimetriche
Il moto per curvatura media a volume costante è l'evoluzione di una ipersuperficie con velocità data dalla curvatura media, con un termine aggiuntivo non locale tale che il volume racchiuso resti costante. Il termine non locale crea delle difficoltà aggiuntive, ad esempio non è più valido il principio di confronto. D'altra parte, il rapporto isoperimetrico della regione racchiusa decresce nel tempo nel flusso a volume costante, a differenza di quanto accade nel flusso ordinario. La monotonia del rapporto isoperimetrico fornisce un utile strumento per studiare il comportamento per tempi grandi e la convergenza a un profilo sferico delle ipersuperfici convesse. Tale approccio è stato generalizzato recentemente ad altri flussi a volume costante, con velocità date da funzioni più generali delle curvature principali, o dalla curvatura media frazionaria. Questi risultati sono ottenuti in collaborazione con M.C. Bertini, E. Cinti ed E. Valdinoci.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 28 marzo 2023
Ore 14:30, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma"Tor Vergata"
Seminario di Analisi Matematica
Francesca Oronzio (Università di Roma "Sapienza")
ADM mass and potential theory
In this talk, we describe some monotonicity formulas holding along the regular level sets of suitable p-harmonic functions in asymptotically flat Riemannian 3-manifolds with a single end, with or without boundary, having nonnegative scalar curvature. Using such formulas, we obtain some geometric inequalities, including the positive mass inequality and the Riemannian Penrose inequality.
Martedì 28 marzo 2023
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Ulrich Kraehmer (TU Dresden)
What is a quantum group?
In this talk I will explain what a quantum group (Hopf algebra) is, but from a slightly nonstandard point of view that focuses on their actions on other algebras. The main objective is to then discuss actions of quantum groups on singular plane curves that turn the latter into quantum homogeneous spaces. Based on joint work with Angela Tabiri, Manuel Martins, and Blessing Oni.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 29 marzo 2023
Ore 9:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Aleksey Sikstel (University of Cologne)
Approximate half-Riemann solvers for coupled of hyperbolic PDE
Modelling of gas networks, fluid-structure systems and multi-phase flows requires development of coupling techniques. Recent works on coupling of hyperbolic systems of conservation laws based on solving two half Riemann problems require expensive iterative procedures at every quadrature point. The natural step to increase its performance is approximating the solutions of the half Riemann problems using techniques established for finite-volume methods. In this work we investigate approximate-state solvers for coupled systems of hyperbolic conservation laws and their applications.
Mercoledì 29 marzo 2023
Ore 11:00, Aula Dal Passo, Tor Vergata
Seminario RoMaDS
Francesco Grotto (Università di Pisa)
Random Waves, Oscillatory Integrals and Random Walks
We consider Random Wave models, that is probability distributions on Laplacian eigenfunctions, on homogeneous spaces such as Euclidean spaces, Hyperspheres and Hyperbolic spaces. Determining the asymptotic behavior at large frequency of functionals of these objects is complicated by the oscillatory nature of their covariance functions. Oscillatory integrals appearing in evaluating variances of said functionals turn out to be closely related to integral representations of densities of uniform random walks in Euclidean spaces, and this connection can be exploited to deduce results on fluctuations of integral functionals of Random Waves.
Mercoledì 29 marzo 2023
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Karl-Hermann Neeb (FAU Erlangen-Nürnberg)
Causal symmetric spaces and nets of operator algebras
In the theory of local observables in Algebraic Quantum Field Theory (AQFT) modular theory creates a one-parameter group of modular automorphisms from a single state and this group often has a geometric implementation. If modular groups are contained in finite-dimensional Lie groups, they naturally lead to gradings of the Lie algebra and further to causal symmetric spaces. Conversely, we explain how nets of local observables (resp. of standard subspaces) on causal symmetric spaces can be constructed for all irreducible unitary representations of simple Lie groups which are either linear or locally isomorphic to SL(2,R). This is joint work with Jan Frahm (Aarhus), Gestur Olafsson (Baton Rouge) and Vincenzo Morinelli (Rome)
Per informazioni, rivolgersi a: ruzzi@mat.uniroma2.it
Mercoledì 29 marzo 2023
Ore 16:00, Aula 311, secondo piano edificio C, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario "I Tè di Matematica"
Vincenzo Bonifaci (Università degli Studi Roma Tre)
Algoritmi naturali, computazioni emergenti
Come riesce la muffa mucillaginosa Physarum polycephalum a trovare il cammino più breve in un labirinto, e in generale a costruire reti sorprendentemente efficienti? Illustreremo il concetto di algoritmo naturale, dando una panoramica di come si possa analizzare matematicamente il meccanismo biofisico che consente ad un organismo acellulare di risolvere il problema del cammino minimo in un grafo. Discuteremo inoltre ulteriori problemi computazionali risolubili con algoritmi ispirati dalla natura.
Giovedì 30 marzo 2023
Ore 14:00, Aula 1B1- Pal. RM002 - Via Scarpa, Dipartimento SBAI
Seminario "PDE a tutto SBAI"
Barbara Brandolini (Università di Palermo)
Symmetrization for singular fractional elliptic problems
We provide some symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Some interesting consequences are L^p regularity results and nonlocal energy estimates for solutions.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 30 marzo 2023
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Giovanni Cerulli-Irelli (Sapienza)
Degeneration order for quivers with self-duality
The representation varieties of a Dynkin quiver are examples of affine varieties (actually affine spaces) over which a structure group acts with finitely many orbits, by Gabriel's theorem. To describe orbit closures there are invariants which generalize the usual ranks. After recalling this classical situation, I will consider the case when the quiver is endowed with a self-duality and hence the representation varieties are endowed with an involution: in this case it is interesting to consider the subvariety of fixed points for this involution. It is acted upon by a group that it is the subgroup of fixed points for an involution of the structure group. How can one describe the orbit closures of such fixed points? It turns out that the orbit closures are nothing else than the intersection of the orbit closures for the "big" group with the variety of fixed points. This is the main result that I want to present which I obtained in collaboration with Magdalena Boos (arXiv 2106.08666).
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 30 marzo 2023
Ore 14:45, Aula 1B1, RM002, Via Scarpa, Dipartimento SBAI
Seminario "PDE a tutto SBAI"
Riccardo Molle (Università di Roma "Tor Vergata")
Positive solutions for non-autonomous Schroedinger equations with prescribed mass
This talk concerns with some recent results about the existence of positive solutions with fixed L^2 norm for nonlinear Schrödinger equations with a non-symmetric potential. Mass supercritical and mass subcritical regimes are considered. We describe a nonexistence result and then we present existence results. In particular, the case of exterior domains is analysed, where the result is new also for the autonomous problem. Joint works with T. Bartsch, S. Lancelotti, G. Riey, M. Rizzi and G. Verzini.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 30 marzo 2023
Ore 15:00, Aula Picone (anche a distanza, tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Claudio Bernardi (Sapienza Università di Roma)
I teoremi di Gödel e l’attività matematica
Chi è interessato a partecipare a distanza può rivolgersi ad Annalisa Cusi (annalisa.cusi@uniroma1.it)
Giovedì 30 marzo 2023
Ore 15:45, Aula 1B1, RM002, Via Scarpa, Dipartimento SBAI
Seminario "PDE a tutto SBAI"
Caterina Sportelli (University of Western Australia, Department of Mathematics and Statistics)
New existence results for singular relativistic problems
In this talk we will discuss the existence of T–periodic solutions of two relativistic equations involving singular terms. The first part will deal with the study of the Lorentz force equation in the challenging physical configuration where the electric field possesses a singularity in zero. Here, the existence of a T-periodic solution is achieved by using a variational framework tailored on relativistic problems with singularities. Moreover, we will employ both a variational and a topological argument to prove that a relativistic pendulum-type equation admits at least a T-periodic solution. These results are part of a joint work with David Arcoya.
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Venerdì 31 marzo 2023
Ore 11:00, aula "Roberta Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Corso di dottorato
Martina Lanini (Università di Roma "Tor Vergata")
Springer Correspondence
This course aims to present one of the first results in geometric representation theory: the Springer Correspondence. The goal of geometric representation theory is to study representations of certain algebraic structures (finite Weyl groups, in our case) via geometric methods. Springer’s result (generalised in several ways and still a central tool nowadays) achieves a construction of all representations of a finite Weyl group (e.g. the symmetric group) in terms of the cohomology of a certain variety. The striking point of Springer’s construction is that the Weyl group action he discovers is highly non trivial and hidden, since the Weyl group does not act on the variety itself. Some of the arguments we are going to address are: representation theory of the symmetric group via tableaux combinatorics; flag variety and Bruhat decomposition; nilpotent cone, the Springer resolution, Springer fibres; construction of the Weyl group action on the cohomology of the Springer sheaf. The discussion will be more or less detailed, depending on the participants’ background and interests.
Per informazioni, rivolgersi a: lanini@mat.uniroma2.it
Venerdì 31 marzo 2023
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario MoMA
Simon Guest (University of Cambridge)
Zero-stiffness structures
The talk will provide a compendium of ’zero-stiffness’ structures, describing three classes of structures that remain in a neutral state of equilibrium, even while they undergo large (and clearly geometrically nonlinear) displacements, with part or all of each structure undergoing large (but elastic) deformations. The structures will not be abstract theoretical constructions, but real structures modelled using reasonable assumptions. Physical examples will be demonstrated.
Per informazioni, rivolgersi a: basile@mat.uniroma.it garroni@mat.uniroma1.it
Venerdì 31 marzo 2023
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Giulia Iezzi (Università di Roma "Tor Vergata" & RWTH Aachen University)
A realisation of some Schubert varieties as quiver Grassmannians
Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. For instance, this method was used to study linear degenerations of flag varieties, obtaining characterizations of flatness, irreducibility and normality via rank tuples. We give a construction for smooth quiver Grassmannians of a specific wild quiver, realising a class of Schubert varieties inside flag varieties. This allows for a definition of linear degenerations of Schubert varieties.
Venerdì 31 marzo 2023
Ore 15:00, Aula 1B1, Dipartimento SBAI, Sapienza Università di Roma, Pal. RM002
Algebra e geometria allo SBAI
Stefano Capparelli (Sapienza Università di Roma)
Rappresentazioni di algebre affini e partizioni di interi (e una “lagniappe”)
A partire da una esposizione storica del rapporto tra le rappresentazioni di alcune algebre di Lie e la teoria delle partizioni di interi arriviamo a qualche risultato recente e qualche congettura su identità combinatorie.
Venerdì 31 marzo 2023
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti A.A. 2022-2023
Lorenzo Carlucci (Università Roma Sapienza) (Università Roma Sapienza)
Indecidibilità algoritmica e auto-referenza
Venerdì 31 marzo 2023
Ore 16:00, Aula Roberta "Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Elena Pascucci (Sapienza Università di Roma)
Fundamental Superalgebras in PI Theory
Fundamental superalgebras are special finite-dimensional superalgebras over an algebraically closed field of characteristic zero defined in terms of certain multialternating graded polynomials. They play a key role in Kemer's Representability Theorem. In the present talk we provide new examples of fundamental superalgebras. Finally, if time allows, we shall give a characterization of fundamental superalgebras in terms of the representation theory of the hyperoctahedral group. This is based on a joint work with Antonio Giambruno and Ernesto Spinelli.
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