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Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 03-03-2025 al 09-03-2025
Lunedì 03 marzo 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Davide Barilari (Università di Padova)
Towards unified synthetic curvature bounds for Riemannian and sub-Riemannian geometry
The Lott-Sturm-Villani theory of CD(K, N) metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense via optimal transport, though extremely successful, has been shown not to directly apply to sub-Riemannian geometries. Nonetheless, still using optimal transport tools, some entropy inequalities have been proved to hold in the case of the Heisenberg group and more in general in sub-Riemannian manifolds. In this talk we survey the known results and motivate a new approach we propose aiming to unify Riemannian and sub-Riemannian synthetic Ricci lower bounds, introducing suitable curvature dimension conditions. (joint with Andrea Mondino (Oxford) and Luca Rizzi (SISSA)) This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Lunedì 03 marzo 2025
Ore 15:00, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Discussione di tesi di Dottorato (Geometria algebrica)
Nelson Alvarado (Tor Vergata)
Cohomological rank functions and Seshadri constants on abelian varieties
In this thesis we study some questions on abelian varieties by means of the Fourier-Mukai-Poincaré (FMP) transform and generic vanishing. Specifically, we study cohomological rank functions, and give a reinterpretation of them in terms of Mukai's semi-homogeneous vector bundles. On the other hand, we introduce the theory of vanishing thresholds of coherent sheaves, extending the notion of basepoint-freeness threshold. In particular, we obtain a sensible notion of jets-separation thresholds of a polarization and relate them to a more classical invariant, namely the Seshadri constant of the polarization. In addition, we establish certain dualities, coming from the FMP transform, which give relations between thresholds on an abelian variety and thresholds on its dual. As concrete applications, we describe obstructions for a polarization to be normally generated and prove a result about the surjectivity of certain higher Gauss-Wahl maps, which allow us to show that the failure of the surjectivity of some of these maps characterize special kinds of abelian varieties.
Lunedì 03 marzo 2025
Ore 15:30, CU36, Dipartimento di Matematica, Sapienza Università di Roma
Working Seminar
Alice Callegaro (Technische Universität München)
Critical branching random walk
Martedì 04 marzo 2025
Ore 10:30, sala conference, INdAM Piazzale Aldo Moro, 5 – Roma
LYSeMinar
Xavier Venel (Luiss University)
Uniform value in stochastic games
I will present an introduction to the literature on dynamic problem s controled by several agents, called Stochastic games and in particular on the concept of uniform value (two-player zero-sum case). We will first review the positive results of the literature if the players observe everything before investigating the many difficulties that appear when the players do not observe everything but only some signals.
Per informazioni: https://www.altamatematica.it/lysm/lyseminar/
Martedì 04 marzo 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Adriana Garroni (Sapienza Università di Roma)
Grain boundaries in polycrystals: the role of topological defects
Locally periodic structures show regions (grains) with different orientations and at the boundaries between grains there is the appearance of defects. This happens in physical systems (for instance at microscopic scales for metals or patterns in block copolymers) as well as in more geometric models (as local tassellations for partions and clusters, or optimal location problems). In all these cases the energy governing the systems concentrates at the grain boundaries. The understanding of this “surface tesion” is a key ingredient in order to reduce the complexity of the problem and work in a so to say sharp interface model. I will present some recent results in this direction focussing on a two dimensional model for grain boundaries in metals, which account for the elastic long range distorsion due to the presence of crystal defects (dislocations). The latter is inspired to a recent model proposed by Lauteri and Luckhaus. Its asymptotics as the lattice spacing tends to zero produces a sharp interface model for grain boundaries which confirms the Read-Shockley law for small angle grain boundaries. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Martedì 04 marzo 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Teoria Dei Numeri e Geometria
Nicolas Mascot (Trinity College Dublin)
Algorithms for plane algebraic curves, with an application to integrating algebraic functions
We will outline an efficient algorithmic approach to the desingularisation of plane algebraic curves. Applications include computing the genus, Riemann-Roch spaces, and testing whether the curve is hyperelliptic. Afterwards, we will see that the (apparently rustic-looking) problem of finding the antiderivative of an algebraic function is actually related to the (much cooler-sounding) ability to test whether certain divisors are torsion in the Picard group of a curve. We will show how to achieve this thanks to the algorithms outlined earlier, which will lead us to a complete integration algorithm for algebraic functions based on arithmetic geometry. The talk will feature many explicit examples.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 05 marzo 2025
Ore 13:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario del ciclo MATHtalks
Danilo Gregorin Afonso (Università di Urbino)
Introduction to Spectral Geometry, or "how to hear the shape of a drum"
Heat diffusion, wave propagation (drums, guitars), electric and magnetic phenomena, quantum stuff, fluid flow... all these physical phenomena share the property of being modelled by partial differential equations (PDEs) where a major role is played by the Laplace operator, thus understanding its properties is very important. One main feature is that it can be "diagonalized", which means solving the PDE (called Hemholtz equation) −∆ψ = λψ, with boundary conditions that depend on the physical context, where both the number λ and the function ψ are unknowns. These two entities dictate much of the behavior of those physical problems. All these things depend very strongly on the shape of the domain where the problem is posed, so a number of questions arise: how does one compute λ, and what are the domains of a given volume that minimize/maximize it? How does λ depend on the size of the domain? Can we find general rules to estimate λ? Does λ have any general properties? What is the behavior of ψ in terms of the sign? How do different solutions (λ, ψ) compare to each other? What is the influence of the boundary conditions on all this stuff? What do all these words even mean? To answer these questions, a number of very interesting theories were invented, and very curious results were proved. This talk, besides introducing the main concepts, aims at exposing these surprising results and apparatus, avoiding technicalities (a.k.a. proofs) but discussing the ideas instead, as well as bringing you into contact some background instruments that should be part of the toolbox of any person interested in analysis. We will also explore some physical examples.
Mercoledì 05 marzo 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Domenico Valloni (EPFL Lausanne)
Classi di Brauer supersingolari in caratteristica positiva
Lo scopo di questo talk è di definire e studiare certe classi di Brauer in caratteristica positiva che si possono costruire dalle forme differenziali. Dopo aver spiegato la costruzione e le prime proprietà di questi oggetti, dimostreremo che il gruppo di Brauer delle superfici K3 supersingolari può essere ottenuto in questo modo. Se il tempo permette, parleremo anche del ruolo che queste classi hanno nell'ostruzione di Brauer-Manin al principio locale-globale.
Mercoledì 05 marzo 2025
Ore 14:30, Aula Seminari, Dipartimento di Scienza di Base e Applicate per l'Ingegneria, Sapienza Università di Roma
Seminario Gruppo UMI-Climath
Giuseppe Attanasi (Sapienza, Dipartimento di Economia e Diritto)
Beyond the threshold: how electoral size-dependent uncertainty affects majority determination
Per informazioni, rivolgersi a: fabio.camilli@uniroma1.it
Mercoledì 05 marzo 2025
Ore 14:30, aula 116, primo piano, IAC-Cnr, via dei Taurini 19, 00185 Roma e streaming al link https://www.youtube.com/watch?v=Nlfp5GliC_E
Seminario straordinario
Youssef Khalifeh (Lebanese University, hadat)
A new Extended KDV Equation: Theoretical Study, Numerical Validation & Tsunami Application
The KdV is one of the most widespread non-linear models, commonly used by coastal engineers, describing the propagation waves in weakly non-linear and weakly dispersive shallow water problems. Many oceanographical applications are represented by this equation such as tsunami waves. Over the last few decades, the derivation of the extended KdV equation has been studied extensively. However, these equations have rarely been derived rigorously. The first aim of this work is to give insight into their rigorous mathematical derivation, instead of only referring to it. We will present here a rigorous derivation of an extended KdV equation on the velocity. With this aim in mind, the primary research method for this paper will depend on the definition of consistency. Hence, a rigorous justification of new extended KdV equations will be provided thanks to this definition. This result provides a precise mathematical answer to a question raised by several authors in recent years, that is the verification of the extended KdV equations, derived previously, using formal methods. The second goal is to derive new linear asymptotical models of the extended KdV equation and then Boussinesq equations so that they have the same accuracy as the standard models. We solve explicitly these new linear models and numerically validate the results. An application for tsunami waves is also presented.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 05 marzo 2025
Ore 15:30, Aula Seminari, Dipartimento di Scienza di Base e Applicate per l'Ingegneria, Sapienza Università di Roma
Seminario gruppo UMI-Climath
Claudia Ceci (Sapienza, Dipartimento di Metodi e Modelli per l'Economia, il Territorio e la Finanza)
Optimal prevention strategies for reducing claim frequency in risk models with jump clusters
Per informazioni, rivolgersi a: fabio.camilli@uniroma1.it
Mercoledì 05 marzo 2025
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Alessandro Olgiati (Politecnico di Milano)
One-body tunneling at the many-body level: excitation spectrum of a Bose gas in a double well
An interacting many-particle quantum system can be drastically affected by a change in the magnitude of one-particle tunneling across a potential barrier. The results which we will present are part of a long-term effort which aims at addressing such a phenomenon. In spite of the huge literature on Schroedinger operators with potential barriers, the influence of tunneling on many-body systems has been little explored so far. We will show that elementary excitations of an interacting Bose gas trapped by a double-well potential are much larger than the one-body gap. The effective model ruling the excitation spectrum is a suitable two-mode Bose-Hubbard Hamiltonian. This will be framed in the context of Bogoliubov's theory. Joint work with Simone Rademacher (LMU Munich) and Nicolas Rougerie (ENS Lyon).
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Giovedì 06 marzo 2025
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di modellistica differenziale numerica
Michael Dumbser (Università di Trento)
On well-balanced finite volume and discontinuous Galerkin schemes for the Einstein-Euler system of general relativity
We present a new family of well-balanced discontinuous Galerkin (DG) finite element schemes with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Einstein-Euler Z4 system, which is composed of 64 equations, is analysed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows. We furthermore present a novel family of central WENO finite difference schemes for a new first order reformulation of the classical BSSNOK system. All standard tests of numerical relativity are successfully reproduced, reaching four main achievements: we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; a (standard) TOV star under perturbation is evolved in pure vacuum (ρ = p = 0) up to t = 1000 with no need to introduce any artificial atmosphere around the star; and, we solve the head on collision of two punctures black holes, that was previously considered untractable within the FO-Z4 formalism, we perform a stable long-time evolution of a rotating binary black hole merger based on the new CWENO schemes for first order reformulation of the BSSNOK system.
Giovedì 06 marzo 2025
Ore 14:15, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Philipp Habegger (University of Basel)
The transfinite diameter of finite trees and dynamical Schinzel-Zassenhaus
In 2019, Dimitrov proved the Schinzel-Zassenhaus Conjecture. Harry Schmidt and I showed how his general strategy can be adapted to cover some dynamical variants of this conjecture. One common tool in both results is Dubinin's Theorem on the transfinite diameter of hedgehogs. Motivated by Mahler's work on root separation, I gave an elementary proof of Dubinin's Theorem, albeit with a worse numerical constant. In this talk, I will report on joint work in progress with Harry Schmidt. We find new upper bounds for the transfinite diameter of some finite topological trees. We construct these trees using the Hubbard tree of a post-critically finite map. They are more attuned to the dynamical setting than hedgehogs. As a consequence, we can cover new cases of the dynamical Schinzel-Zassenhaus Conjecture.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 06 marzo 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Nathanaël Boutillon (INRAE - Aix Marseille Univ)
A principal eigenvalue problem for a strongly anisotropic second-order elliptic operator
I will talk about a principal eigenvalue problem for a second-order elliptic operator with a very small diffusion coefficient in one direction. In this regime, how do the principal eigenvalue and the principal eigenfunction behave? To handle the interaction between the slow and fast variables, I will use a representation of the principal eigenfunction as a quasi-stationary distribution of a killed process. Next, in some particular cases, I will give the limit of the principal eigenvalue when the diffusion coefficient converges to zero in one direction.
This seminar is part of the activities of the PRIN project 2022W58BJ5 PDEs and optimal control methods in mean field games, population dynamics and multi-agent models, funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: galise@mat.unroma1.it
Venerdì 07 marzo 2025
Ore 11:30, Aula D'Antoni , Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata
DocTorV Seminar
Giulia Iezzi (Roma Tor Vergata/RWTH Aachen)
An introduction to quiver Grassmannians
We will introduce quiver representations and quiver Grassmannians, focusing on the fact that "quiver Grassmannians can be anything" - that is, every projective variety is a quiver Grassmannian. The goal of this seminar is to discuss a few existing applications and examples of the study of quiver Grassmannians, in particular their applications to linear degenerations of flag varieties and of Schubert varieties, highlighting how these projective varieties are related to the underlying quiver representation theory.
Per informazioni, rivolgersi a: doctorv.uniroma2@gmail.com
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