Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 17-03-2025 al 23-03-2025

Lunedì 17 marzo 2025
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Mariapia Palombaro (Università de L’Aquila)
Differential inclusions and polycrystals
We discuss a differential inclusion arising in the context of bounding effective conductiv- ities of polycrystalline composites. The datum is a set of three positive numbers identified with a positive definite diagonal matrix S. The aim is to find suitable solutions to the inclusion DU ∈ K := {λR^t S R : λ ∈ R, R ∈ SO(3)}. We will show how to construct a class of so-called approximate solutions via infinite-rank laminations. The resulting average fields provide an inner bound for the quasi-convex hull of K, which is an improvement of the bounds that were previously established by Avellaneda et al. [1] and Milton & Nesi [2]. We will also discuss some open problems related to the lack of outer bounds and the existence of exact solutions to the differential inclusion. This is joint work with N. Albin and V. Nesi. References [1] M. Avellaneda, A. V. Cherkaev, K. A. Lurie, G. Milton. On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality. J. Appl. Phys. 63, 4989–5003, 1988. [2] V. Nesi, G. Milton. Polycrystalline configurations that maximize electrical resistivity. J. Mech. Phys. Solids no. 4, 525–542, 1991. 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 17 marzo 2025
Ore 15:00, Aula 1B, Palazzina RM002, Dipartimento SBAI, Via A. Scarpa 16
Corso di Dottorato
Marta Menci (Università Campus Bio-Medico di Roma)
Modelling and Simulations of Collective Dynamics - Lecture 1
The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of global patterns from local interactions can be easily observed in flock of birds, schools of fish, human crowds, but also cells exhibit collective behaviors in different biological processes characterizing the human body (e.g. in embryogenesis, wound healing, immune response, tumor growth). The main feature of collective cells migration is that the emergent behavior is also driven by chemical stimuli, and not only by mechanical interactions. This course aims to give participants a brief but complete introduction to the research field of modelling and simulation of collective dynamics. Starting with a survey of influential works of the literature, recent mathematical developments and new directions and applications will be presented. A specific focus will be on different numerical techniques proposed to simulate the different kind of equations involved in the presented models.
Per informazioni, rivolgersi a: marta.menci.mm@gmail.com

Lunedì 17 marzo 2025
Ore 17:00, aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Matematica, Scienza & Società
Michela Procesi (Università di Roma Tre)
Moti ricorsivi e stabilità nei sistemi dinamici
Uno dei problemi fondamentali della meccanica è descrivere matematicamente i moti, per esempio il moto planetario o delle particelle in un fluido. A parte esempi specialissimi però, non ci si può aspettare di poter dare una descrizione esatta del comportamento in ciascun istante. In effetti in generale le evoluzioni temporali possono essere molto imprevedibili, ad esempio, in assenza di attrito, ci si aspetta la coesistenza di dinamiche ricorrenti e caotiche. In questo seminario discuterò principalmente modelli semplificati che sono piccole perturbazioni di sistemi di molle e mostrerò che già in questo caso si osservano vari fenomeni matematicamente interessanti e fisicamente significativi.
Per informazioni, rivolgersi a: enrico.rogora@uniroma1.it

Martedì 18 marzo 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Gianmaria Verzini (Politecnico di Milano)
Singular analysis of a shape optimization problem arising in population dynamic
When analyzing the survival threshold for a species in population dynamics, one is led to consider the principal eigenvalue of some indefinite weighted problems in a bounded domain. The minimization of such eigenvalue, associated with either Dirichlet or Neumann boundary conditions, translates into a shape optimization problem. We perform the analysis of the singular limit of this problem, in case of arbitrarily small favorable region. We show that, in this regime, the favorable region is connected, and it concentrates at points depending on the boundary conditions. Moreover, we investigate the interplay between the location of the favorable region and its shape. Joint works with Lorenzo Ferreri, Dario Mazzoleni and Benedetta Pellacci.
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Martedì 18 marzo 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Geometria
Grigory Mikhalkin (Université de Genève)
Vitruvian polygons in symplectic problems
Each angle formed by two rays with integer slopes has two basic integer invariants: its height and its width. An angle is called Vitruvian (after a Roman architect Vitruvius advocating proportions between height and width) if its height divides its length. A Vitruvian polygon is a polygon, such that all of its angles are Vitruvian. Vitruvian polygons form a distinguished class of polygons in Tropical Planimetry. After a breakthrough idea of Galkin and Usnich from 2010, Vitruvian triangles (studied, under a different guise, by Hacking and Prokhorov, buiding up on an earlier work of Manetti to obtain the complete classification of toric degenerations of the plane) started to play a prominent role also in Symplectic Geometry. In the talk, I review some of these applications, as well as a new symplectic application, involving use of Vitruvian quadrilaterals (work in progress, joint with Richard Hind and Felix Schlenk).
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com

Mercoledì 19 marzo 2025
Ore 13:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario del ciclo MATHtalks
Riccardo Bernardini (Sapienza Università di Roma)
Introduzione ai campi quadratici reali
I campi quadratici reali, dati dall'aggiunta a \(\mathbb{Q}\) della radice quadrata di un numero positivo che non sia lui stesso un quadrato, sono uno degli oggetti centrali della Teoria dei Numeri classica e sono collegati a questioni che vanno indietro di secoli, almeno fino ai lavori di Gauss. Il seminario si propone di introdurre alcuni degli strumenti più importanti per lo studio dei campi quadratici reali, come frazioni continue e carattere di Krönecker, e di presentare la formula del numero di classe la quale, coinvolgendo le quantità più significative del campo, è ancora oggi fulcro di vivace ricerca.
Per informazioni, rivolgersi a: MATHtalks@uniroma1.it

Mercoledì 19 marzo 2025
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Tuan Ngo Dac (Université de Caen)
On moduli spaces of shtukas
In this talk we give an overview of the geometry of moduli spaces of shtukas for the general linear groups GL(n). These moduli spaces have been instrumental in the work of Drinfeld and Lafforgue on the Langlands correspondence for GL(n) over function fields. We then explore the connection between the geometry of these moduli spaces and the wonderful compactification of De Concini-Procesi. This talk is based on joint work with Y. Varshavsky.

Mercoledì 19 marzo 2025
Ore 15:00, Aula 1B, Palazzina RM002, Dipartimento SBAI, Via A. Scarpa 16
Corso di Dottorato
Marta Menci (Università Campus Bio-Medico di Roma)
Modelling and Simulations of Collective Dynamics - Lecture 2
The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of global patterns from local interactions can be easily observed in flock of birds, schools of fish, human crowds, but also cells exhibit collective behaviors in different biological processes characterizing the human body (e.g. in embryogenesis, wound healing, immune response, tumor growth). The main feature of collective cells migration is that the emergent behavior is also driven by chemical stimuli, and not only by mechanical interactions. This course aims to give participants a brief but complete introduction to the research field of modelling and simulation of collective dynamics. Starting with a survey of influential works of the literature, recent mathematical developments and new directions and applications will be presented. A specific focus will be on different numerical techniques proposed to simulate the different kind of equations involved in the presented models.
Per informazioni, rivolgersi a: marta.menci.mm@gmail.com

Mercoledì 19 marzo 2025
Ore 16:15, Aula I piano, IAC-CNR, Via dei Taurini 19, Roma
Seminari Vito Volterra
Paolo Buttà (Sapienza Università di Roma)
Time evolution of concentrated vortex rings
The motion of fluids can sometimes be effectively modeled by a finite-dimensional dynamical system. A paradigmatic example is the point vortex model, introduced by Helmholtz in a seminal paper, which describes a regime where the vorticity of an ideal, incompressible fluid is confined to a set of infinitely thin, straight, parallel vortex filaments. In this talk, I will present recent results concerning an incompressible, inviscid fluid with axial symmetry and no swirl, establishing a connection between the motion of a system of N concentrated vortex rings with large radii and a dynamical system closely related to the point vortex model. Based on joint work with Guido Cavallaro and Carlo Marchioro.
Per informazioni, rivolgersi a: lucia.deluca777@gmail.com

Giovedì 20 marzo 2025
Ore 14:00, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Concettina Galati (Calabria)
About deformations of surfaces in P^3 which are singular along a line
We will report about a jont work in progress with Ciro Ciliberto about deformations to nodal surfaces of surfaces in P^3 which are double along a line.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Giovedì 20 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
Kevin Payne (Università degli Studi di Milano)
The Correspondence Principle: A bridge between general potential theories and nonlinear PDEs
General potential theories concern the study of functions which are subharmonic with respect to a suitable constraint set in the space of 2-jets. While interesting in their own right, general potential theories are being widely used to study fully nonlinear PDEs determined by degenerate elliptic operators acting on the space of 2-jets. We will discuss a powerful tool, the Correspondence Principle, which establishes the equivalence between subharmonics/superharmonics u and admissible subsolutions/supersolutions u (in the viscosity sense) of the PDE determined by every operator which is compatible with the constraint set. The crucial degenerate ellipticity often requires the operator to be restricted to a suitable constraint set, which determines the admissibility. Applications to comparison principles by way of the duality-monotonicity-fiberegularity method will also be discussed. The results to be presented have been obtained in collaboration with Marco Cirant, Reese Harvey, Blaine Lawson and Davide Redaelli.
This talk is part of the activity of the research Project : PRIN 2022 PNRR project 2022AKNSE4 "Variational and Analytical aspects of Geometric PDEs" , founded by the European Union- Next Generation EU.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it

Giovedì 20 marzo 2025
Ore 15:00, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Alice Garbagnati (Milano)
Singular symplectic surfaces
There are several possible generalizations of the definition of irreducible holomorphic symplectic manifold to the singular context (primitive symplectic variety, irreducible symplectic orbifold, irreducible symplectic variety). We review these definitions and we consider them in the lowest dimensional case, i.e. the case of the surfaces. We classify the surfaces which satisfy these definitions, showing that all of them are contractions of rational curves on K3 surfaces, but that not all the possible contractions of rational curves on K3 surfaces satisfy all these definitions. Then we consider the Hilbert scheme of points of the singular surfaces considered, and we show that in some specific cases they are irreducible symplectic orbifolds. The talk is based on a joint work with M. Penegini and A. Perego.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Venerdì 21 marzo 2025
Ore 10:30, Aula B2, blocco aule, Dipartimento di Matematica e Fisica, Università Roma Tre
Difesa tesi di Dottorato
Simone Pesatori (Roma Tre)
Curves on Enriques surfaces and on rational elliptic surfaces
We explore the geometry of the Enriques surfaces and of the rational elliptic surfaces, particularly focusing on the genus 1 pencils they admit, on the Severi varieties of curves on them and on the rational curves lying on them. We investigate the open problem of the existence of rational curves in the very general Enriques surface: exploiting the "regeneration" results due to Chen, Gounelas and Liedtke about curves on K3 surfaces and a construction of some particular Enriques surfaces by Hulek and Schütt, we prove that for every \( k\equiv_4 1 \), the very general Enriques surface admits rational curves of arithmetic genus \( k \) and \( \phi=2 \) .

Venerdì 21 marzo 2025
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata
DocTorV Seminar
Francesco Malizia (Scuola Normale Superiore)
Critical metrics on closed manifolds
One of the main goals of Riemannian geometry is to understand the relationship between the geometry and topology of smooth manifolds. To achieve this, it is useful to look for "canonical metrics" encoding the most significant topological information about a manifold. Among these metrics, we have the so-called critical metrics, which are critical points of specific curvature functionals. After introducing these objects, we will focus on the 4-dimensional case and explore the challenges associated with finding critical metrics through a direct variational approach. No previous knowledge will be assumed.
Per informazioni, rivolgersi a: doctorv.uniroma2@gmail.com

Venerdì 21 marzo 2025
Ore 16:00, Aula Enriques, Dipartimento di Matematica, Sapienza Università di Roma
Conferenze PLS per docenti
Stefano Finizi Vita (Sapienza Università di Roma), Davide Passaro (Liceo Russel) & Davide Palmigiani (ITIS e Liceo Scientifico Scienze Applicate Vallauri, Velletri)
Spunti per introdurre alcuni concetti base dell'intelligenza artificiale in un liceo matematico

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