Notiziario Scientifico

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

Settimana dal 27-01-2025 al 02-02-2025

Lunedì 27 gennaio 2025
Ore 11:30, Aula C, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale 84
Seminario di Fisica Matematica
Eris Runa (GSSI L'Aquila)
Pattern formation and symmetry breaking for a family of functionals with isotropic local/nonlocal interactions
In this talk, we will introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. More precisely, we consider a general class of nonlocal variational problems in dimension \(d\geq 1\), in which an isotropic surface term favouring pure phases competes with an isotropic nonlocal term with power law kernel favouring alternation between different phases. Close to the critical regime in which the two terms are of the same order, we give a rigorous proof of the conjectured structure of global minimizers, in the shape of domains with flat boundary (e.g. stripes or lamellae). The natural framework in which our approach is set and developed is the one of calculus of variations and geometric measure theory. This work is in collaboration with S. Daneri.

Lunedì 27 gennaio 2025
Ore 9:00:, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Calculus of Variations and PDE's in Geometric Analysis
9:00 Registration & Welcome 10:00 Topping 11:30 Tonegawa 14:00 Carlotto 15:00 Bellettini 16:30 Pluda See https://sites.google.com/uniroma1.it/cvga2025/conference for more information. 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 through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Martedì 28 gennaio 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Alex Casarotti (Università degli Studi di Ferrara)
On unirationality of conic bundles with 8 singular fibers
We investigate the problems of unirationality and rationality for conic bundles \(S \to \mathbb{P}^1\) over a C1 field k, which can be described as the zero locus of a hypersurface in the projectivization of a rank-3 vector bundle over \(\mathbb{P}^1\). Conic bundles can be classified by the degree d of the discriminant, i.e. the number of points on the base where the corresponding fiber is not a smooth conic. Unirationality for d < 8 was already established by Kollár and Mella in 2014, while the case for general d remains open. In this work we focus on the next case d=8, and explicitly show that for all four possible types of such conic bundles S, the set of unirational ones forms an open subset of the parameter space. We also examine algebraic constraints, depending on the base field k, under which a general S is not rational over k.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com

Martedì 28 gennaio 2025
Ore 9:00:, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma)
Calculus of Variations and PDE's in Geometric Analysis
9:00 Del Pino 10:30 Franz 11:30 Agostiniani 14:00 Tarantello 15:30 Laurain See https://sites.google.com/uniroma1.it/cvga2025/conference for more information. 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 through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Mercoledì 29 gennaio 2025
Ore 15:00, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di Dipartimento
Felix Schulze (University of Warwick, UK)
Mean curvature flow with generic initial data
Mean curvature flow is the gradient flow of the area functional where an embedded hypersurface evolves in direction of its mean curvature vector. This constitutes a natural geometric heat equation for hypersurfaces, which ideally will evolve the embedding into a nicer shape. But due to the nonlinear nature of the equation singularities are guaranteed to form. Nevertheless, a key observation in geometry and physics is that generic solutions, obtained by small perturbations, can exhibit simpler singularities. In this direction, a conjecture of Huisken posits that a generic mean curvature flow encounters only the simplest singularities. We will discuss work together with Chodosh, Choi and Mantoulidis which together with recent work of Bamler-Kleiner establishes this conjecture for embedded hypersurfaces in R³.
N.B.Questo colloquium fa parte delle attività del "MIUR Excellence Department Project MATH@TOV CUP E83C23000330006"

Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Mercoledì 29 gennaio 2025
Ore 16:00, Aula M1, Dipartimento di Matematica e Fisica, Università di Roma Tre, Lungotevere Dante 376
Colloquium di Matematica
Marcel Guardia (Universitat de Barcelona)
Unstable motions in Celestial Mechanics
One of the oldest problems in dynamical systems is the stability of the Solar System. That is, consider N bodies moving following Newton's law of gravitation, one of them with large mass (the Sun) and the others with small masses (the planets). If one neglects, the gravitational interaction between planets, the classical Kepler's laws assert that the planets move on ellipses. Then, one wants to understand whether the effect of the planet's mutual attraction causes long term changes on the shape and relative position of the Keplerian ellipses. Nowadays, it is known that the answer to the stability of the Solar system is rather nuanced and that stability and instability coexist for nearby initial conditions. In this talk I will explain how to construct unstable motions in this model, which lead to drastic changes in the semimajor axes, eccentricity and inclination of these ellipses.

Mercoledì 29 gennaio 2025
Ore 16:45, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Operator Algebra Seminar
Filippo Bracci (University of Rome Tor Vergata)
The Beurling theorem for finite index shifts and the invariant subspace problem
The famous Beurling theorem provides a concrete characterization of closed invariant subspaces for the shift on the Hardy space H^2 in the unit disc, stating that every such space is of the form fH^2 , where f is an inner function. This result can also be interpreted in an operator sense by saying that every closed subspace invariant for the shift is the image of H^2 via an isometry. From this perspective, Beurling’s theorem has been extended by Lax, Halmos, and Rovnyak to shifts of any index, proving that a closed subspace is invariant for a shift if and only if it is the image of the space via a quasi-isometry that commutes with the shift (the so-called Beurling-Lax theorem). In this talk, I will present a generalization of the “concrete” form of Beurling’s theorem for the shift on the direct finite sum of H^2. I will show that every closed invariant subspace is given, up to multiplication by an inner function, by the intersection of what we call “determinantal spaces”—which, roughly speaking, are the preimages of shift-invariant subspaces of H^2 via a linear operator commuting with the shift and that are constructed through a determinant of certain matrices with entries given by holomorphic bounded functions. The concreteness of such a structure theorem allows us to prove by rather simple algebraic manipulation, as in the classical Beurling theorem, that the only non-trivial maximal closed shift-invariant subspaces are of codimension one. Using the universality of the (backward) shift in the class of operators with defect less than or equal to the index of the shift, this gives a proof of the following result: every bounded linear operator from a Hilbert space into itself whose defect is finite has a non-trivial closed invariant subspace. The talk is based on a joint work with Eva Gallardo-Gutierrez The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0

Mercoledì 29 gennaio 2025
Ore 9:00:, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Calculus of Variations and PDE's in Geometric Analysis
9:00 Chambolle 10:30 Julin 11:30 Masnou See https://sites.google.com/uniroma1.it/cvga2025/conference for more information. 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 through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Giovedì 30 gennaio 2025
Ore 14:15, Aula M4, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Ada Boralevi (Politecnico di Torino)
Spaces of matrices with rank conditions and group actions
A space of matrices of constant rank is a vector subspace V, say of dimension n+1, of the set of matrices of size axb over a field k, such that any nonzero element of V has fixed rank r. It is a classical problem to look for examples of such spaces of matrices, and to give relations among the possible values of the parameters a,b,r,n. In this talk I will report on my latest joint projects (and work in progress) with D. Faenzi, D. Fratila and P. Lella, where we use techniques involving vector bundles on projective spaces, finitely generated graded modules, and representation theory.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Giovedì 30 gennaio 2025
Ore 9:00:, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Calculus of Variations and PDE's in Geometric Analysis
9:00 Pacard 10:30 Zemas 11:30 Hirsch 14:00 Schulze 15:30 Saez See https://sites.google.com/uniroma1.it/cvga2025/conference for more information. 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 through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Venerdì 31 gennaio 2025
Ore 14:30, Aula piano terra IAC CNR, Istituto per le Applicazioni del Calcolo, Cnr, via dei Taurini 19, Roma
Lectio Magistralis di Sauro Succi, Eugenio Beltrami Senior Scientist Prize 2023
Sauro Succi (IIT e IAC-CNR)
Beltrami, Boltzmann and the unreasonable power of lattice kinetic theory
In this talk we shall present an historical survey of the conceptual and computational developments which led to the formulation of the Lattice Boltzmann (LB) method; from its statmech foundations (Lattice Gas Cellular Automata) to present-day leading edge scientific and engineering applications across a broad range of scales and regimes of motion. From large scale turbulent flows, to micro-nanofluids all the way down to quark-gluon plasmas and, recently, quantum computing for fluids as well. These developments, spanning over three decades in time, witness to the outstanding power of (lattice) kinetic theory as a privileged mathematical and computational framework for the quantitative study of complex states of flowing matter far from equilibrium and its multiple applications to modern science and engineering, A remarkable success story that falls perfectly within Eugenio Beltrami’s great legacy.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it

Venerdì 31 gennaio 2025
Ore 16:00, Aula Vito Volterra, Dipartimento di Matematica, Sapienza Università di Roma
Seminari PLS per docenti
Eugenio Montefusco (Sapienza Università di Roma)
Problem solving per le attività di PCTO: alcune esperienze

Venerdì 31 gennaio 2025
Ore 9:00:, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Calculus of Variations and PDE's in Geometric Analysis
9:00 Novaga 10:30 Michelat 11:30 Van Schaftingen See https://sites.google.com/uniroma1.it/cvga2025/conference for more information. 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 through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

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