Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 01-04-2024 al 07-04-2024
Martedì 02 aprile 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.
Martedì 02 aprile 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Martin Fleurial (Sapienza University of Rome)
Two Dimensional Models of Multi-Lane Traffic Flow with Lane Changing Conditions
The first part of the talk is dedicated to the derivation on an advection-diffusion equation in two dimensions from a system of one dimensional hyperbolic PDEs modeling the macroscopic behavior of multi-lane traffic flow, taking lane changes into account. In the second part of the talk, we introduce the microscopic model the latter system originates from, and propose a generalisation of this model to two continuous space dimensions. We discuss its properties and well-posedness.
Martedì 02 aprile 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Donato Scarcella (UPC Barcelona)
Asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, in the present talk, we consider a time-dependent perturbation of a Hamiltonian dynamical system having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of orbits converging in time to the quasiperiodic solutions associated with the unperturbed system. This result generalizes the work of Canadell and de la Llave, where exponential decay in time was considered, and the one of Fortunati and Wiggins, where arithmetic, non-degeneracy conditions, and exponential decay in time are assumed. We apply this result to the example of the planar three-body problem perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit (modeled as a time-dependent perturbation). 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
Mercoledì 03 aprile 2024
Ore 10:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Mercoledì 03 aprile 2024
Ore 13:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Vittoria Silvestri (Università di Roma La Sapienza)
Introduction to Random Geometry
This course wants to give an overview of active research topics in the field of Random Geometry, with a focus on growth models. We will start by discussing discrete growth models such as the Eden model, Diffusion Limited Aggregation and Internal DLA. We will then move to the continuum for the remaining part of the course. After discussing conformal invariance of Brownian motion, we will focus on the class of randomly growing domains on the complex plane which can be described via Loewner dynamics. We will introduce several random aggregation models on the complex plane, which go under the name of Hastings-Levitov models and Aggregate Loewner Evolutions, of which we will study the large-scale features, presenting existing results and several open questions.
Mercoledì 03 aprile 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Leonardo Patimo (Università di Pisa)
Singular Light Leaves
In this talk, we will describe how to construct a basis of Bott-Samelson bimodules, called singular light leaves. Bott-Samelson bimodules are algebraic objects that correspond geometrically to resolutions of singularities of Schubert varieties. In the nonsingular case, that is for Schubert varieties in full flag varieties, Libedinsky introduced a basis (called light leaves) between Bott-Samelson bimodules which has been extensively used to compute the decomposition behavior in the Hecke category, for example enabling the discovery of counterexamples to Lusztig's conjecture on representations in characteristic p. We will thoroughly extend Libedinsky's result to the singular setting. To do this, we will employ the language of diagrammatic calculus associated with Frobenius extensions. Our construction has concrete applications in computing intersection forms, as well as more theoretical implications pointing towards a diagrammatic definition of the Hecke category. This is a joint project with B. Elias, H. Ko, and N. Libedinsky.
Mercoledì 03 aprile 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminari di Algebre di Operatori
Florin Radulescu (Università di Roma Tor Vergata)
Automorphic forms design of free group factors and quantum dynamics
The role of automorphic forms as intertwiners between various representations of free group factors was discovered a long time ago by Vaughan Jones, starting with a remarkable formula relating Peterson scalar product with the intrinsical trace. The intertwiner associated to an automorphic form is an eclectic object, not much can be computed, but the Muray von Neuman dimension can be used to get hints on its image. Vaughan Jones used that to settle the problem of finding analytic functions vanishing on the orbit under the modular group of a point in the upper half plane. In past work of the speaker, it was put in evidence that this is related to equivariant Berezin quantization. This leads to a different representation of free group factors and to the existence of a quantum dynamics whose associated unbounded Hochschild 2- cocycle is related to the isomorphism problem. I will explain some concrete formulae and some new interpretation of the associated quantum dynamics The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Giovedì 04 aprile 2024
Accademia Nazionale dei Lincei, Palazzo Corsini, Via della Lungara 10, Roma
Convegno
La filosofia nella matematica del '900
Programma:
- 10:10-11:00 Michele Ciliberto (Scuola Normale Superiore, Pisa; Linceo) Croce, Enriques, De Sarlo. Filosofia e scienze in Italia all'inizio del '900
- 11:30-12:20 Laura Crosilla (Università degli studi di Firenze) Predicativismo
- 12:30-13:20 Carlo Toffalori (Universitè degli studi di Camerino) La matematica diventa grande
- 15:00-15:50 Gabriele Lolli (Scuola Normale Superiore, Pisa) Modelli di crescita
- 16:10-17:00 Silvia De Toffoli (Scuola Universitaria Superiore IUSS, Pavia) Filosofia della pratica matematica: una panoramica
Giovedì 04 aprile 2024
Ore 14:00, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Lucia Caporaso (Roma Tre)
Hypertangency of curves and a conjecture of Vojta
The talk will report on joint work with Amos Turchet on a standard conjecture of diophantine geometry usually attributed to Vojta. This conjecture predicts that the complement in the complex projective plane of a general nodal curve, B, of degree at least 4 contains finitely many copies of \(\mathbb{C}^*\), where \(\mathbb{C}^*\) is the set of nonzero complex numbers. This is equivalent to the fact that the preimage of B under any non constant map from a smooth rational curve, X, to the plane has cardinality at most 2. Via a purely geometric approach, we prove this conjecture effectively when B has at least three irreducible components, and without the rationality assumption on X.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 04 aprile 2024
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Giulio Tralli (Università degli Studi di Ferrara)
Overdetermined problems tailored for gauge balls
In this talk we discuss a family of overdetermined boundary value problems in the context of the Heisenberg group. We focus on various similarities and differences with respect to the classical symmetry result for the torsion function studied by Serrin. We show uniqueness results for gauge balls under suitable partial symmetry assumptions for the class of competitor sets. The main technical tool is a new Bochner-type identity for functions with toric/cylindrical invariances. This is a joint work with V. Martino.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 04 aprile 2024
Ore 15:00, Aula 5, Dipartimento di Matematica, Sapienza Università di Roma
Corso di dottorato
Guido Pezzini (Sapienza)
Algebre di Hecke
Giovedì 04 aprile 2024
Ore 15:00, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Pietro Corvaja (Udine)
Valori razionali di funzioni razionali
Tratteremo l'immagine per una funzione razionale dell'insieme dei punti razionali di una varietà algebrica; un caso cruciale si realizza quando la varietà algebrica è un gruppo algebrico commutativo. Vedremo che varie questioni in questo ambito si collegano alla proprietà di Hilbert, al principio locale-globale, alla questione della densità di punti interi/razionali su varietà algebriche. I risultati originali sono stati ottenuti in collaborazione con Umberto Zannier.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Venerdì 05 aprile 2024
Accademia Nazionale dei Lincei, Palazzo Corsini, Via della Lungara 10, Roma
Convegno
La filosofia nella matematica del '900
Programma:
- 10:00-10:50 Mario Piazza (Scuola Normale Superiore, Pisa; Linceo) Matematica e spiegazioni
- 11:30-12:20 Gianluigi Oliveri (Università degli studi di Palermo) Sulla filosofia strutturalista della matematica
- 12:30-13:20 Gabriele Pulcini (Università degli studi di Roma Tor Vergata) Purezza e semplicità nel XXIV problema di Hilbert
- 15:00-15:50 Valeria Giardino (CNRS-Institut Jean Nicod, ENS-PSL, Paris) Mente, mondo e matematica: dal naturalismo alle scienze cognitive
- 16:10-17:00 Claudio Fontanari (Università degli studi di Trento) Il Bourbakismo tra filosofia e pratica
Venerdì 05 aprile 2024
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
corso di dottorato
Martina Lanini (Tor Vergata)
Algebre di Hecke
Venerdì 05 aprile 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Seminario di Topologia
Nicolas Guès (U Paris 13)
Homotopical methods in representation stability
For many known families of algebro-geometric objects indexed by natural numbers (symmetric groups, braid groups, ...), a phenomenon known as homological stability happens: their homology H_d(X_n) becomes stationary when n goes to infinity. Sometimes, these objects are equipped with actions of the symmetric group \Sigma_n on X_n: in this context, the right notion of stability is that of representation stability introduced by Church and Farb in 2010. One main example is the family of ordered configuration spaces of manifolds, whose cohomology is known to be representation stable with explicit ranges. I will review in this talk the main ideas of representation stability and explain how we can take a homotopy-theoretic point of view on representation stability to generalize such stability theorems. (This talk is part of the activity of the MIUR Excellence Department Projects MatMod@TOV.)
Venerdì 05 aprile 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti A. A. 2023-2024
Annalisa Malusa, Donatella Ricalzone e Noemi Stivali (Sapienza Università di Roma, IIS Pascal (Roma), Liceo Newton (Roma))
Vito Volterra, chi era costui? Una proposta pluridisciplinare di matematica applicata.
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.