## Weekly Bulletin (it)

**Notiziario dei seminari di carattere matematico**

a cura del Dipartimento di Matematica

*Guido Castelnuovo*, Sapienza Università di Roma

Settimana dal 25-09-2023 al 01-10-2023

**Lunedì 25 settembre 2023**

Ore 15:00, Dal Passo , Dipartimento di Matematica, Università Tor Vergata

Seminario RoMaDS

Marco Carfagnini (University of California San Diego)
*Spectral gaps via small deviations*

In this talk we will discuss spectral gaps of second order differential operators and their connection to limit laws such as small deviations and Chung’s laws of the iterated logarithm. The main focus is on hypoelliptic diffusions such as the Kolmogorov diffusion and horizontal Brownian motions on Carnot groups. If time permits, we will discuss spectral properties and existence of spectral gaps on general Dirichlet metric measure spaces.This talk is based on joint works with Maria (Masha) Gordina and Alexander (Sasha) Teplyaev.

Per informazioni, rivolgersi a: * salvi@mat.uniroma2.it*

**Martedì 26 settembre 2023**

Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Modellistica Differenziale Numerica

Stephan Gerster (University of Mainz)
*Haar-type stochastic Galerkin formulations for random hyperbolic systems*

The idea to represent stochastic processes by orthogonal polynomials has been employed in uncertainty quantification and inverse problems. This approach is known as stochastic Galerkin formulation with a generalized polynomial chaos (gPC) expansion. The gPC expansions of the stochastic input are substituted into the governing equations. Then, they are projected by a Galerkin method to obtain deterministic evolution equations for the gPC coefficients. Applications of this procedure have been proven successful for diffusion and kinetic equa- tions. So far, results for general hyperbolic systems are not available. A problem is posed by the fact that the deterministic Jacobian of the projected system differs from the random Jacobian of the original system and hence hyperbolicity is not guaranteed. Applications to hyperbolic conservation laws are in general limited to linear and scalar hyperbolic equations. We analyze the loss of hyperbolicity for isentropic Euler equations. In particular, hy- perbolicity depends on the choice of gPC expansion. In particular, the dependency on a random input is described by Haar-type wavelet systems. Theoretical results are illus- trated numerically by CWENO-type reconstructions combined with a numerical entropy indicator that allow also for higher-order discretizations of balance laws.

**Martedì 26 settembre 2023**

Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"

Seminario di equazioni differenziali

Jonathan Ben-Artzi (Cardiff University (UK))
*Quantifying the complexity of everyday computations: from abstract ideas to applications in spectral theory*

In the first part of this talk I will present the Solvability Complexity Index — a theory developed with several coauthors over the last decade to help us classify the complexity of everyday computations. This theory serves as a bridge between classifications of degrees of complexity in theoretical computer science, and applications in numerical analysis. In the second part of the talk, I will discuss recent results where these ideas were applied to the computation of resonances, providing the first algorithms that work in any dimension. Note: This talk is part of the activities supported by the MIUR Department of Excellence Project MatMod@TOV (2023-2027)

Per informazioni, rivolgersi a: * sorrentino@mat.uniroma2.it*

**Mercoledì 27 settembre 2023**

Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Algebra e Geometria

Sebastian Goette (Universität Freiburg)
*Homotopy Associative Submanifolds in G2-manifolds*

Associative submanifolds are certain calibrated submanifolds in \(G_2\)-manifolds. There is the hope that counting them will reveal subtle information about the underlying \(G_2\)-structure. On the other hand, certain singular associatives can be resolved in exactly three different ways, so a naive count will be meaningless. In this talk, we will define homotopy associatives as cobordism classes of threedimensional submanifolds that are adapted to the \(G_2\)-structure in a rather weak sense. We will see that a given cobordism class can be interpreted as a homotopy associative in exactly three different ways. This might help us to define a consistent counting scheme even when the naive number of associatives in a given cobordism class changes due to singularities.

**Giovedì 28 settembre 2023**

Ore 14:30, Aula 1/B1, Dipartimento SBAI, Via Scarpa 12, Dipartimento SBAI

Seminario di Analisi Matematica

Manuel del Pino (University of Bath (UK))
*Gluing methods in the Water Wave Problem*

In the classical Water Wave Problem, we construct new overhanging solitary waves by a procedure resembling desingularization of the gluing of constant mean curvature surfaces by tiny catenoidal necks. The solutions here predicted have long been numerically detected. This is joint work with Juan Davila, Monica Musso, and Miles Wheeler.

Per informazioni, rivolgersi a: * massimo.grossi@uniroma1.it*

**Giovedì 28 settembre 2023**

Ore 16:00, Aula 1B1 (pal. RM002), Dipartimento SBAI, Sapienza Università di Roma

Algebra e Geometria allo SBAI

Jack Allsop (Monash University)
*Latin squares without proper subsquares*

A Latin square of order \(n\) is an \(n \times n\) matrix of \(n\) symbols, such that each symbol occurs exactly once in each row and column. A subsquare of order \(k\) is a \(k \times k\) submatrix of a Latin square that is itself a Latin square. Every Latin square of order \(n\) contains \(n^2\) subsquares of order one, and one subsquare of order \(n\). All other subsquares are called proper. If a Latin square contains no proper subsquares then it is called \(N_\infty\). Around 50 years ago Hilton conjectured that an \(N_\infty\) Latin square of order \(n\) exists for all sufficiently large \(n\). Hilton’s conjecture was previously known to hold for all integers \(n\) not of the form \(2^a3^b\) for integers \(a \geq 1\) and \(b \geq 0\). We resolve Hilton’s conjecture by constructing\(N_\infty\) Latin squares for the remaining orders.

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*.

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