Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 13-05-2024 al 19-05-2024
Lunedì 13 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Simone Fagioli (Università De L'Aquila)
Aggregation-Diffusion model for opinion formation on networks
We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolution of the agents on the network. Firstly, we apply the Deterministic Particle Approximation (DPA) method to the aforementioned system in order to prove the existence of solutions under suitable assumptions on the interactions between agents. Later on, we present an explicit model for opinion formation on an evolving network. The opinions evolve based on both the distance between the agents on the network and the 'attitude areas,' which depend on the distance between the agents' opinions. The position of the agents on the network evolves based on the distance between the agents' opinions. The goal is to study radicalization, polarization, and fragmentation of the population while changing its open-mindedness and the radius of interaction. Joint work with Gianluca Favre. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Lunedì 13 maggio 2024
Ore 17:30, Sala A, Cnr Biblioteca Centrale "G. Marconi" P.le Aldo Moro, 7 00185 Roma
Celebrating Women in Mathematics May12th
Roberta Bianchini, Chiara de Fabritiis, Pegah Moshir Pour (V.V.)
Donne nella matematica
In occasione dell'evento internazionale May12 Celebrating Women in Mathematics, giornata internazionale delle donne nella matematica, l'Unità pianificazione, programmazione e Biblioteca Centrale e l'Istituto per le applicazioni del calcolo "M. Picone" (Iac) del Cnr hanno organizzato l'evento "Donne nella matematica" che si terrà il 13 maggio, presso la sala A della Biblioteca Centrale "G. Marconi" alle ore 17.30. Ogni anno in tutto il mondo vengono organizzati eventi locali o virtuali che si svolgono nel periodo compreso tra il 1° maggio e il 15 giugno, con l’obiettivo di incoraggiare la diversità e superare i pregiudizi di genere, esaltare i successi delle ricercatrici in matematica, anche per guidare e stimolare le giovani donne che vogliono studiare questa disciplina. La manifestazione May12, giunta alla sua 6a edizione, è stata istituita il 31 luglio 2018 durante il "World Meeting for Women in Mathematics" e si è scelta proprio questa data perché ricorre il giorno del compleanno di Maryam Mirzakhani, la prima donna ad aver ottenuto la medaglia Fields, uno dei più ambiti riconoscimenti in matematica. L'evento sarà moderato da Silvia Bencivelli, giornalista e divulgatrice scientifica. Interverranno: Roberta Bianchini, ricercatrice Cnr-Iac, Chiara de Fabritiis, coordinatrice del Comitato per le pari opportunità dell'Unione matematica italiana, Pegah Moshir Pour, attivista per i diritti umani e digitali. Info e registrazione: https://registrazioneeventi.cnr.it/event/72/
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Martedì 14 maggio 2024
Ore 14:00, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Valeria Bertini (Università di Genova)
Deformation families of IHS varieties: classification problem and new examples
A fruitful way to produce examples of IHS varieties is to consider terminalizations of symplectic quotients of symplectic varieties. In a work in collaboration with A. Grossi, M. Mauri and E. Mazzon we classify all terminalizations of quotients of Hilbert schemes of K3 surfaces and generalized Kummer varieties by the action of symplectic automorphisms induced by the underlying surface. Furthermore, we determine their second Betti number, the fundamental group of their singular locus and, in the Kummer case, we determine the singularities of their universal quasi-étale cover. Finally, we compare our deformation types with the examples known in literature, placing our work in the classification program proposed by Menet.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 14 maggio 2024
Ore 14:30, Aula M2, Dipartimento di Matematica e Fisica, Università di Roma Tre, Lungotevere Dante 376
seminario di Probabilità
Federico Sau (Università degli Studi di Trieste)
Scaling limits of the averaging process
The averaging process on a graph is a continuous-space Markov chain, which is commonly interpreted as an opinion dynamics, a distributed algorithm, or an interface moving through a randomized sequence of deterministic local updates. Its dynamics goes as follows. Attach i.i.d. Poisson clocks to edges, and assign real values to vertices; at the arrival times of these clocks, update the values with their average. As time runs, the averaging process converges to a flat configuration, and one major problem in the field is that of quantifying the speed of convergence to its degenerate equilibrium in terms of characteristic features of the underlying graph.
In this talk, after reviewing some basic properties and recent results on mixing times for the averaging process on general graphs, we focus on the discrete d-dimensional torus, and on some finer properties of the process in this setting. We discuss some quantitative features (e.g., limit profile, early concentration and local smoothness), and look at nonequilibrium fluctuations, a particularly interesting problem in this degenerate context lacking a non-trivial notion of local equilibrium. If time permits, we will touch on the main ideas of the proof of such scaling limits, which combine tools from Malliavin calculus in Poisson space, their probabilistic dynamic interpretations, and some new discrete-gradient estimates. Talk based on the preprints arXiv.2311.14176, arXiv.2403.02032.
Martedì 14 maggio 2024
Ore 16:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Michele Coti Zelati (Imperial College, London)
Diffusion and mixing for two-dimensional Hamiltonian flows
We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular flow on a periodic box, and explore potential consequences for the long-time dynamics in the two-dimensional Euler equations.
NB: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Martedì 14 maggio 2024
Ore 17:30, Aula C, Dipartimento di Matematica, Sapienza Università di Roma
YAMS - Young Algebraist Meetings in Sapienza
Giuseppe Bargagnati ( Università di Bologna)
Bounded cohomology of discrete groups and quasimorphisms
Bounded cohomology of groups was introduced by Johnson and Trauber in the 70's, and has developed as a research topic of independent interest after Gromov's pioneering article of 1982 "Volume and bounded cohomology". Since then, it has been expoited in different areas, such as geometric group theory, topology and geometry of manifolds, actions on the circle and characteristic classes. In this seminar, I will define bounded cohomology of discrete groups and see how it is related with the usual cohomology of groups. Moreover, we will explore the relationship between bounded cohomology in degree two and quasimorphisms.
Mercoledì 15 maggio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Roberto Pirisi (Università di Napoli Federico II)
Brauer groups of moduli problems and enumerative geometry
The Brauer group, classifying Azumaya algebras up to Morita equivalence, is a fundamental invariant in number theory and algebraic geometry. Given a moduli problem M (e.g. smooth curves of a given genus, K3 surfaces, abelian varieties of a given dimension...) one can consider an element of the Brauer group of M as a way to functorially assign to any family X -> S in M(S) an element in the Brauer group of S. If we consider the moduli problem M_g of smooth curves of a given genus, the Brauer groups of M_{1,1} (the moduli problem of elliptic curves) and M_2 are known over a vast generality of bases, for example Br(M_{1,1}) is known when the base is any field or the integers; the Brauer group of M_g for g at least 4 is known to be trivial over the complex numbers through topological methods. The case g=3 is open over any base. In a recent paper with Andrea di Lorenzo (Università di Pisa) we show that over any field k of characteristic zero the Brauer group of M_3 is equal to a direct sum of Br(k) and a copy of Z/2Z. To our surprise, the proof of this result goes through one of the most well-known theorems in classical enumerative geometry: there are exactly 27 lines lying on a cubic surface in P^3. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Mercoledì 15 maggio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Agostino Patella (Humboldt Universität zu Berlin, Institut für Physik & IRIS Adlershof)
Extracting Scattering Amplitudes from Euclidean Correlators
Scattering amplitudes can be extracted from time-ordered n-point functions by means of the well known LSZ reduction formula, even in non-perturbative Quantum Field Theories, such as Quantum Chromodynamics (QCD). However, in the context of Lattice QCD, one can access only Euclidean n-point functions sampled at discrete points and with finite (but systematically improvable) precision and accuracy. This makes the problem of analytically continuing back to Minkowski space-time ill-posed. I will present here one particular strategy which allows to extract scattering amplitudes from Euclidean correlators, while avoiding analytic continuation, technically turning an ill-posed problem into a merely ill-conditioned one. Working in the axiomatic framework of the Haag-Ruelle scattering theory, we show that scattering amplitudes can be approximated arbitrarily well in terms of linear combinations of Euclidean correlators at discrete time separations. The essential feature of the proposed approximants is that one can calculate them, at least in principle, from Lattice-QCD data. In this talk, after reviewing the basic ideas behind Haag-Ruelle scattering theory, I will sketch the derivation of the approximations formulae, and discuss extensively how they can be used in practical numerical calculations. Also, similarities and differences with other methods, e.g. Lüscher's formalism, will be reviewed. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Mercoledì 15 maggio 2024
Ore 15:00, Aula B, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale 84, e via Teams al seguente link
Doppio Seminario di Analisi e Fisica Matematica
- 15:00 Seminario di Analisi: Fernando Argentieri (Zurich) KAM beyond Bryuno condition
For one dimensional dynamical systems it is well know from the work of Yoccoz that the optimal arithmetic condition to bypass the small divisor problem in the analytic class in the local setting (for example to analytically linearize circle analytic diffeomorphisms that are close to a rotation) is the so called Bryuno condition. In a joint work with Livia Corsi we provide an arithmetic condition that is weaker then the Bryuno condition for which it is still possible to bypass the small divisor problem in higher dimension. The scheme will be provided for analytic diffeomorphisms of the Torus that are close to a rotation and for which the rotation vector exists.
- 16:15 Seminario di Fisica Matematica: Christian Hainzl (Munich) The Gell-Mann—Brueckner formula for the correlation energy of the mean-field Coulomb gas
I will present recent joint work with M. Christiansen and P. T. Nam. We consider a fermionic system interacting via Coulomb potential, scaled by \(k_F= N^{1/3}\), denoted as mean-field Coulomb, on the unit periodic box. We establish the analog of the Gell-Mann—Brueckner formula. More precisely, we show that the correlation energy is of the form \(c_1 k_F \log k_F + c_2 k_F + o(k_F)\) for specific constants \(c_1, c_2\), where \(k_F\) is the Fermi-momentum.
Mercoledì 15 maggio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario Algebre di Operatori
Giulio Codogni (Università di Roma Tor Vergata)
Vertex algebras and Teichmüller modular forms
Vertex algebras are algebraic structures coming from two dimensional conformal field theory. This talk is about their relation with moduli spaces of Riemann surfaces. I will first review some background material. In particular, I will recall that a vertex algebra is a graded vector space V with additional structures, and these structures force the Hilbert-Poincaré series of V, conveniently normalized, to be a modular form. I will then associate to any holomorphic vertex algebra a collection of Teichmüller modular forms (= sections of powers of the lambda class on the moduli space of Riemann surfaces), whose expansion near the boundary gives back some information about the correlation functions of the vertex algebra. This is a generalization of the Hilbert-Poincaré series of V, it uses moduli spaces of Riemann surfaces of arbitrarily high genus, and it is sometime called partition function of the vertex algebra. I will also explain some partial results towards the reconstruction of the vertex algebra out of these Teichmüller modular forms. Using the above mentioned construction, we can use vertex algebras to study problems about the moduli space of Riemann surfaces, such as the Schottky problem, the computation of the slope of the effective cone, and the computation of the dimension of the space of sections of powers of the lambda class. On the other hand, this construction allows us to use the geometry of the moduli space of Riemann surfaces to classify vertex algebras; in particular, I will discuss how conjectures and known results about the slope of the effective cone can be used to study the unicity of the moonshine vertex algebras. This is a work in progress with Sebastiano Carpi. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Mercoledì 15 maggio 2024
Ore 16:15, sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Raffaele Scandone (Università di Napoli)
Growth of Sobolev norms for a quantum fluid system
I will discuss the existence of turbulent solutions to a quantum hydrodynamic (QHD) system, with periodic boundary conditions. A suitable nonlinear change of variables (the Madelung transform) formally connects the QHD system to a non-linear Schrödinger (NLS) equation, for which we can construct smooth solutions displaying arbitrarily large growth of Sobolev norms above the energy regularity level. This amounts to a cascade in time of the energy to higher Fourier modes. In addition, these solutions can be designed to be small amplitude perturbations of stationary states, which implies in particular absence of quantum vortices. This allows to exploit an equivalence between high regularity QHD- and NLS- norms, which eventually yields the existence of smooth, turbulent solutions to the quantum hydrodynamic system. Based on joint work with F. Giuliani Il seminario si svolgerà all'interno delle attività del progetto PRIN 2022CHELC7 "Singular Interactions and Effective Models in Mathematical Physics" finanziato dall’Unione europea – Next Generation EU.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Giovedì 16 maggio 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Aaron Levin (Michigan State)
Diophantine Approximation to Closed Subschemes
The classical Weil height machine associates heights to divisors on a projective variety. I will give a brief introduction to this machinery, how it extends to objects (closed subschemes) in higher codimension, due to Silverman, and present various ways to interpret the heights. We will then discuss several recent results in Diophantine approximation in which these ideas play a prominent and central role.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 16 maggio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p): Problemi differenziali nonlineari/Nonlinear differential problems
Luigi Muglia (Università della Calabria)
Optimal second order boundary regularity for solutions to p-Laplace equations
Solutions to \(p\)-Laplace equations are not, in general, of class\( C^2\). The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz’ya shows that, if the source term is in \(L^2\), then the field \(|\nabla u|^{p−2}\nabla u\) is in \(W^{1,2}\). The \(L^2\)-regularity of the source term is also a necessary condition. During the talk, following a paper in collaboration with Luigi Montoro and Berardino Sciunzi, we will obtain under suitable assumptions, sharp second order estimates, thus proving the optimal regularity of the vector field \(|\nabla u|^{p−2}\nabla u\), up to the boundary.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 16 maggio 2024
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università degli Studi d Roma "Tor Vergata"
Evento May 12: Celebrating Women in Mathematics
Cristiana De Fabritis (Università di Parma)
Hybrid perturbations in elliptic regularity
(Opening address: Isabeau Birindelli, Sapienza Università di Roma)
Giovedì 16 maggio 2024
Ore 16:00, Aula Enriques, Dipartimento di Matematica, Sapienza Università di Roma
Colloquium di Dipartimento
Laure Saint Raymond, (Institut des Hautes Études Scientifiques)
Internal waves in a domain with topography
Stratification of the density in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting properties. In particular, in 2D these waves concentrate on attractors for some generic frequencies of the forcing. At the mathematical level, this behaviour can be analysed in the inviscid case with tools from geometry, spectral theory and micro local analysis.
Venerdì 17 maggio 2024
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminari di dottorato
- 9:00-9:40 Giovanna Andreucci: On the nonlinear thin obstacle problem
The thin obstacle problem or n-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic energies, whereas only partial results have been proved in the nonlinear case. In this seminar we consider the thin boundary obstacle problem for a general class of nonlineraities and we prove the optimal \(C^{1,1/2}\)-regularity of the solutions in any space dimension.
- 9:45 - 10:25 Andrea Drago: Volume entropy as a large scale analogue of negative curvature
The interplay between metric and topology has been explored for more than a century, and has driven mathematical research in various fields. A classical example of this relationship is given by the Uniformization Theorem of closed surfaces. For more general manifolds such a complete classification is out of reach, but there are many results that describe how constraints on the metric impose constraints on the topology, and vice versa. We will focus on the negative curvature setting, where the topology is more complex, from a metric perspective. After reviewing some classical theorems we will define a volume entropy as the asymptotic exponential growth rate of the volume of balls in the universal cover with respect to their radius. This quantity can be thought of as a mean, asymptotic version of the Ricci curvature, so we will outline some the entropy analogues of the classical theorem, showing how the entropy can be a measure of the topological complexity. In the end there will be space for one final remark regarding the climate crisis, and the role of our research in such a key moment of history.
- 10:45 - 11:25 Azzurra Ciliberti: Categorification of cluster algebras of type B and C through symmetric quivers
After recalling the combinatorial definition by generators and relations of cluster algebras of type A, B and C, we will state a cluster expansion formula for cluster algebras of type B and C in terms of cluster variables of type A. Then, we will explain how to associate a symmetric quiver Q to any cluster of a cluster algebra of type B and C. Under this correspondence, cluster variables of type B (resp. C) correspond to orthogonal (resp. symplectic) indecomposable representations of Q.
- 11:30 - 12:10 Giacomo Hermes Ferraro: Serie alla Eisenstein nei moduli di Drinfeld
La teoria dei moduli di Drinfeld, sviluppata da Anderson e Thakur negli anni 90, è concepibile come un analogo in caratteristica finita della teoria delle curve ellittiche di variabile complessa, dove il ruolo dell'anello degli interi \(\mathbb Z\) è svolto dall'anello delle funzioni regolari di una curva proiettiva liscia \(X/F_q\) fuori da un punto razionale \(\infty\). Le somme di Gauss-Thakur, analogo delle somme di Gauss, sono interpolate da cosiddette "funzioni speciali", funzioni analitiche su un cambio base di \(X\setminus\infty\). In questa presentazione, parlerò della relazione di queste funzioni con serie "alla Eisenstein", e ne esplorerò il significato.
- 12:15 - 12:55 Luca Casarin: Factorization structures and a factorizable Feigin-Frenkel theorem
The talk will be divided into two main parts. In the first one I will introduce the concept of a factorization structure on a vector bundle on a manifold. This is a rather recent notion which applies in several geometric contexts and sheaf theories and through time has found connections to the representation theory of quantum groups, the theory of chiral algebras (a geometric version of the theory of vertex algebras) and last but not least the notion of an \(E_n\) algebra in homotopical contexts. In the second part we will then move to discuss the Feigin-Frenkel theorem about the center of the enveloping algebra of the affine algebra at the critical level and a factorization (in the above sense) version of it which was part of my PhD project.
- 13:00 - 13:40 Matteo Micheli: A symplectic problem on special quiver Grassmannians
In this talk we will review the basics on quiver Grassmannians, and study a family of projective varieties with some very good properties. Then we consider subvarieties defined by symplectic conditions, and see which of those properties still hold true for the subvarieties.
Venerdì 17 maggio 2024
Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
DocTorV Seminar
Gabriele Bocchi (PhD student, Università Tor Vergata )
The optimal transport problem: equivalent formulations and regularizations
In the first part of the talk we will look at the optimal transport problem from two different approaches, analyzing some of their strengths, weaknesses and sketching the intuitions behind each one. Such approaches will be: the classic Monge-Kantorovich formulation and the Eulerian point of view given by the Benamou-Brenier formulation. In the second part the classical Schrödinger problem will be presented, and we will see how this problem from statistichal mechanics can be seen as a regularization of the optimal transport problem.
Per informazioni, rivolgersi a: vicari@mat.uniroma2.it
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