Universidad de Granada

Motivados por el teorema de semiespacio clásico de Hoffman y Meeks para superficies mínimas en \(\mathbb{R}^3\), el objetivo de esta charla es obtener resultados de tipo semiespacio para superficies inmersas en el espacio Euclideo \(\mathbb{R}^3\) cuya curvatura media viene dada por una función predeterminada dependiendo de su aplicación de Gauss.

25 de octubre de 2019, 11:30, Seminario 1ª planta IEMath-GR

04 de julio de 2019, 10:00, Seminario 1ª planta IEMath-GR

4 de julio de 2019, 10:00, Seminario 1ª planta IEMath-GR

GEOMETRY SEMINAR

Speaker: Jorge Hidalgo (Universidad de Granada)

Abstract: In a recent work with A.Alarcón and I.Castro-Infantes we show that every open Riemann surface admits a complete conformal CMC-1 (constant mean curvature one) immersion in the three dimensional hyperbolic space. In this talk I aim to explain the main ideas in the proof of this result, which relies on the holomorphic representation of CMC-1 surfaces given by Robert Bryant in 1987, and applies modern complex analysis techniques.

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Jose Manuel Muñoz Fuentes (UGR)

Abstract: The theory on error-correcting block codes focuses on how to identify and, if possible, fix errors that might be inserted into fixed-length messages while being sent or stored. Rank codes, which have notable applications on network coding, are known to provide a convenient way to do so. Our approach generalizes the classical family of maximum-rank-distance Gabidulin codes into a larger one, which is endowed with a Hartmann-Tzeng-like lower bound on their rank (and Hamming) distance. For these codes, we develop a syndrome-based error correction algorithm up to the known Hartmann-Tzeng-like bound by decomposing the error-correcting problem into solvable solvable linear algebra ones, including the skew-feedback shift-register synthesis problem. This approach also generalizes previous work on error correction algorithms over skew Reed-Solomon codes (that is, skew-cyclic codes with a Reed-Solomon-like defining set), as those are a subset of the ones studied through our approach.

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Niccolò Tassi (Universidad de Granada)

Absract: We present a nonlocal Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium independent of the non-locality of the equation. This uniform estimate cannot be easily obtained with standard inequalities or entropy methods, but can be obtained through the use of Harris’s theorem, a tool coming from porbability. We point out some interesting links to quantitative versions of the central limit theorem in probability. We also carry out a study of the properties of the stationary states of the problem, especially the behavior of its tails using various techniques.

YOUNG RESEARCHERS MATH SEMINAR

Conferenciante: Gerardo García Moreno (Universidad de Granada)

Abstract: General Relativity is the most succesful theory we have for describing gravitational phenomena. Its range of applicability is vast: from solar system scales to cosmological scales. It is well-known that GR allows the existence of time machines: devices that are able to generate Closed-Timelike-Curves (CTCs). Although these kind of objects are allowed in GR, most researchers believe that they cannot occur on macroscopic scales. However, it is widely believed that a full quantum theory of gravity would be required to fully understand the mechanisms beneath this "Chronology Protection Conjecture". In this talk, I will describe the status of this conjecture within the context of analogue gravity. Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically condensed matter systems, with the aim of gaining new insights into their corresponding problems. There exists a huge catalogue of analogue models: from classical and quantum fluids to optic systems.

After briefly reviewing the role of time machines and the Chronology Protection Conjecture in General Relativity and introducing the analogue gravity program, I will jump to discuss the content of our last paper: arXiv:2201.11072 [gr qc]. We examine carefully whether it is possible to simulate these kind of spacetimes with CTCs within analogue gravity. Although I will focus the discussion on a concrete analogue system, sound waves propagating on top of a Bose Einstein condensate, I will explain the extension of our results to other kind of analogues.

Algebra seminar

Speaker: Tamar Mesablishvili ( Universidad de Granada)

Abstract: Factorizations of mathematical objects is an important topic in Mathematics. The factorization problem consists of both finding all the factorizations of a given mathematical object through its subobjects, and studying properties of a mathematical objects in terms of the two smaller subobjects through which it is already factorized. It occurs frequently that it is possible to solve the initial problem for these subobjects, for which one has techniques that weren’t available for the initial object. Therefore, the factorization problem is crucial and it is being studied and researched in many different fields of Mathematics. Our goal was to describe the set of all possible factorizations of a given monoid. Two necessary and sufficient conditions in terms of so-called descent 1-cocyles for a monoid to be factorized through two submonoids were found. A full classification of those factorizations of a monoid whose one factor is a subgroup of the monoid was obtained.

Differential equations seminar

Speaker: Juan Silverio (Universidad de Granada)

ABSTRACT: In this preliminary work we will concern about the "Finite Morse Index" scenario (instead of the usual stability one) of the following long-standing conjecture: "Let u be a (compactly supported) weak stable solution of the general non-linear Poisson equation and assume that the non-linearity is positive, non-decreasing, convex, and superlinear at +∞, and let n10. Then u is bounded." Recently, Cabré, Figalli, Ros-Oton and Serra end up a complete proof in the classical stability setting: W^{1,2}-stable solutions are universally bounded for n10 (and therefore smooth by classical elliptic regularity theory); namely they are bounded in terms only of their L^1 norm, with a constant that is independent of the non-linearity. This conjecture is in a sense equivalent to another problem stated before by Brezis: Is it possible to prove that the extremal solution of the so-called Gelfand problem is smooth at least in low dimensions?. We will take this as the starting point to reproduce our new results recovering the existing results by S. Villegas in the (semi-)stable case. Using some estimates on the "size" of the local stability behavior of finite Morse Index solutions we provide a uniform a priori bound and some pointwise estimates of that solutions that partially answer positively the long standing conjecture in this more general setting.