## Notiziario Scientifico

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

Settimana dal 11-03-2019 al 17-03-2019

Lunedì 11 marzo 2019
Ore 11:30, Aula C, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario
Jose Ramon Espinosa
A Fresh Look at the Calculation of Tunneling Actions
The calculation of tunneling actions, that control the exponential suppression of the decay of metastable phases (like the unstable electroweak vacuum), can be reformulated as an elementary variational problem in field space. This alternative approach circumvents the use of bounces in Euclidean space by introducing an auxiliary function, a tunneling potential Vt that connects smoothly the metastable and stable phases of the field potential V. The tunneling action is obtained as the integral in field space of an action density that is a simple function of Vt and V and can be considered as a generalization of the thin-wall action to arbitrary potentials. This formalism provides new handles for the theoretical understanding of different features of vacuum decay, can be easily extended to include gravitational effects in an elegant way and has a number of useful applications that I will discuss.

Lunedì 11 marzo 2019
Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Alessandro Audrito (DISMA, Politecnico di Torino)
Asymptotic behaviour of nonlinear flows in tubular domains
We investigate the asymptotic behaviour for large times of solutions to the p-Laplacian diffusion equation posed in a tubular domain, when $$p>2$$, i.e., the slow diffusion case, and homogeneous Dirichlet boundary conditions on the tube boundary. Passing to suitable re-scaled variables, we show the existence of a travelling wave solution in logarithmic time that connects the level $$u = 0$$ and the unique nonnegative steady state associated to the re-scaled problem posed in a lower dimension. This is a joint work with Prof. Juan Luis Vazquez (Universidad Autonoma de Madrid).

Lunedì 11 marzo 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Colloquium di Dipartimento
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
Kazhdan-Lusztig Theory
The study of continuous actions of groups like $$GL(n;\mathbb{R})$$ and $$GL(n;\mathbb{C})$$ on Banach spaces leads to interesting algebraic questions. This field has seen great progress recently, and I want to talk on it.

Martedì 12 marzo 2019
Ore 14:30, Aula 311, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Fisica Matematica
G. Antinucci (University of Zurich)
A hierarchical supersymmetric model for weakly disordered 3d semimetals
An important open problem in quantum mechanics is to prove that noninteracting, disordered 3d quantum systems exhibit a localization-delocalization transition as a function of the disorder strength. From a mathematical viewpoint, a lot is known about the localized phase for strong disorder, much less about the delocalized phase at small disorder. In this talk I will present results for a hierarchical supersymmetric model for a class of disordered 3d gapless quantum systems, called Weyl semimetals. In the absence of disorder, the main feature of these systems is the pointlike nature of the Fermi surface. We use rigorous renormalization group methods to compute the correlation functions of the system. In particular, I will present a theorem about the algebraic decay of the averaged two-point correlation function, compatible with delocalization. Our method is based on a rigorous implementation of renormalization group, reminiscent of the Gawedzki-Kupiainen block spin transformations; the main technical novelty is the multiscale analysis of massless Gaussian measures with purely imaginary covariances. Joint work with Luca Fresta and Marcello Porta.

Martedì 12 marzo 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Analisi Matematica
Alessandra Lunardi (Università di Parma)
Sobolev and BV functions in infinite dimension
In Hilbert or Banach spaces X endowed with a good probability measure $$\mu$$ there are a few "natural" definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals mainly with Gaussian measures and Sobolev and BV functions defined in the whole X, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian measures, is largely to be developed. As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations. In this talk I will describe some of the main features and open problems concerning such function spaces.

Martedì 12 marzo 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellista Differenziale Numerica
Lehel Banjai (Maxwell Institute for Mathematical Sciences, Heriot-Watt University)
Tensor Finite Element Methods for the Spectral Fractional Laplacian
In this talk we discuss the analysis and fast implementation of numerical algorithms for the solution of fractional linear elliptic problems on a bounded domain with a homogeneous Dirichlet boundary condition. We focus on the spectral fractional Laplacian and the corresponding Caffarelli-Silvestre extension. We make use of tensor product finite element spaces with $hp$ finite elements in the extended direction and piecewise linear or $hp$ finite elements in the bounded domain and prove convergence estimates. We describe fast methods for solving the resulting linear system resulting in algorithms of almost optimal complexity. Numerical results will be shown that confirm the theoretical predictions.

Mercoledì 13 marzo 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Nima Moshayedi (Università di Zurigo)
Globalization of Nonlinear AKSZ Sigma Models in the BV-BFV Formalism
We'll give an introduction to the BV-BFV formalism and discuss the setting of certain AKSZ theories. Moreover, we'll describe a globalization procedure using concepts of formal geometry, which extends the Quantum Master Equation for manifolds with boundary. If time permits, we'll also talk about the special case of the Poisson Sigma Model and the relational symplectic groupoid construction of the globalization of Kontsevich‘s star product.

Mercoledì 13 marzo 2019
Ore 9:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
School
Variational approaches to PDE's

• 09:30 - 11:00 Tristan Rivière, Minmax methods for the area of surfaces I
• 11:00 - 11:30 Coffee break
• 11:30 - 12:00 Dario Mazzoleni, Asymptotic spherical shapes in some spectral optimization problems
• 12:00 - 12:30 Roberta Musina, Some advances on Arnold's problem about the existence of multiple K-magnetic geodesics
• 12:30 - 14:00 Lunch break
• 14:00 - 15:30 Thomas Bartsch, Normalized solutions of nonlinear Schrödinger equations and systems I
• 15:30 - 16:00 Break
• 16:00 - 17:30 Tristan Rivière, Minmax methods for the area of surfaces II

Giovedì 14 marzo 2019
Ore 9:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
School
Variational approaches to PDE's

• 09:30 - 11:00 Thomas Bartsch, Normalized solutions of nonlinear Schrödinger equations and systems II
• 11:00 - 11:30 Coffee break
• 11:30 - 12:00 Alessandro Pigati, Parametrized 2D stationary varifolds and the multiplicity one conjecture
• 12:00 - 12:30 Pieralberto Sicbaldi, Overdetermined elliptic problems in exterior domains
• 12:30 - 14:00 Lunch break
• 14:00 - 15:30 Tristan Rivière, Minmax methods for the area of surfaces III
• 15:30 - 16:00 Break
• 16:00 - 17:30 Thomas Bartsch, Normalized solutions of nonlinear Schrödinger equations and systems III

Giovedì 14 marzo 2019
Ore 14:30, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario P(n)/N(p)
Alessandro Fortunati (Università di Bristol)
A local stability result for travelling waves over arbitrary bathymetries
A linear model arising from a shallow-water approximation of the travelling wave problem in a semi-infinite channel is studied in the presence of real-analytic quasi-flat bathymetries. We discuss how to determine the streamfunction by means of constructive methods in a perturbative setting. A result for aperiodically time-dependent systems in finite dimension by Fortunati and Wiggins (2016), is applied in order to conclude on the stability of the streamlines in a neighbourhood of an elliptic equilibrium for the fluid flow.

Giovedì 14 marzo 2019
Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Geometria
Gabriel Dill (University of Basel)
Unlikely intersections with isogeny orbits
In the spirit of the Mordell-Lang conjecture, we consider the intersection of a closed irreducible algebraic subvariety $$V$$ of a non-isotrivial abelian scheme over a smooth irreducible base curve with the images of a finite-rank subgroup $$\Gamma$$ of a fixed abelian variety $$A$$ under all isogenies between $$A$$ and some member of the family, where everything is defined over the field of algebraic numbers. After excluding certain degenerate cases, the André-Pink-Zannier conjecture predicts that this intersection is not Zariski dense in $$V$$. We present our results towards and sometimes beyond this conjecture under restrictions on either the dimension of $$V$$ or the abelian scheme and $$A$$.

Venerdì 15 marzo 2019
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario per Insegnanti (Piano Lauree Scientifiche)
Giovanni Organtini (Dipartimento di Fisica, Sapienza Università di Roma)
La lingua dell'Universo

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