Activities

Let M be a properly embedded, connected, complete surface in R^3 with boundary a convex planar curve C, satisfying an elliptic equation H=f(H^2-K), where H and K are the mean and the Gauss curvature respectively – which we will refer to as Weingarten equation. In this talk, we discuss how the symmetries of C may induce symmetries of the whole M. When M is contained in one of the two halfspaces determined by C, we give sufficient conditions for M to inherit the symmetries of C. In particular, when M is vertically cylindrically bounded, we get that M is rotational if C is a circle. In the case in which the Weingarten equation is linear, we give a sufficient condition for such a surface to be contained in a halfspace. Both results are generalizations of results of Rosenberg and Sa Earp, for constant mean curvature surfaces, to the Weingarten setting. In particular, our results also recover and generalize the constant mean curvature case.

In this talk, I will describe a classification result for translating solitons of the mean curvature flow under two natural quantitative/topological assumptions: finite genus and entropy equal to 2. Roughly speaking, these hypotheses place the translator at the borderline between the simplest nontrivial singularity models and genuinely higher–complexity behavior: finite genus controls the global topology, while the entropy bound rigidifies the possible asymptotic geometry and rules out many exotic configurations. I will explain how one combines geometric measure theory and PDE tools for the translator equation to extract strong structural information from the entropy constraint, leading to a precise description of all such examples. Along the way, I will discuss the role of blow-down and compactness arguments, how the entropy pinching interacts with curvature and topology, and what the result says about the landscape of low-entropy translators. This is joint work with E. S. Gama and N. M. Møller.

📅 jueves 12 de febrero — 12:00

📍 Aula A25, Facultad de Ciencias

👤Conferenciante: Claudia Peña (BCAM)

📖 Título: On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in $\mathbb{R}^3$

📄 Resumen

Seminario de jóvenes investigadores

Fecha y hora: martes 10 de febrero, 10:00

Lugar: Seminario 1, IMAG

Ponente: Inmaculada Benítez Berral (Universidad de Granada)

Title: Convergence to equilibrium for the linear Becker-Döring equations

Abstract: More info

• Seminario de Ecuaciones Diferenciales

We prove the existence of complete minimal surfaces, in Euclidean 3-space, of arbitrary positive genus and least total absolute curvature that have precisely two ends: a catenoidal end and an Enneper-type end. This talk is based on a joint work with Rivu Bardhan, Indranil Biswas, and Pradip Kumar. https://arxiv.org/abs/2509.03925

• IMAG Functional Analysis Seminar
• Title: El teorema de Rademacher en espacios métricos.
• By Iván Caamaño (IMPAM, Poland)
• Abstract: En esta charla abordaremos diferentes variantes del teorema clásico de Rademacher en el contexto de espacios de medida métricos. Se revisarán brevemente algunos de los resultados fundamentales de Kirchheim y Cheeger en esta dirección. Además, consideraremos la noción de diferenciabilidad métrica definida en términos de cartas de Lipschitz del espacio, y sus conexiones con las propiedades de rectificabilidad del espacio subyacente. La charla se basa en un trabajo conjunto con E. Durand-Cartagena, J.Á. Jaramillo, A. Prieto y E. Soultanis.

• Seminario de jóvenes investigadores
• Fecha y hora: martes 9 de diciembre, 10:00
• Lugar: Seminario 2, IMAG
• Ponente: Niccolô Tassi (Universidad de Granada)
• Title: Asymptotic behaviour of Nonlocal and Kinetic equations
• Abstract: Understanding the long-time dynamics of partial differential equations is essential for predicting how these models evolve, assessing their stability, and detecting critical phenomena such as blow-up or bifurcations. In this talk, I will discuss the asymptotic behaviour of certain nonlocal and kinetic equations, which can roughly be divided into confining and non-confining types. In the confining case, where a stationary state exists, various analytical techniques allow one to establish quantitative convergence results. I will present some recent results obtained with José Cañizo (Granada), where we apply Harris’s theorem to prove a uniform spectral gap for a family of nonlocal approximations of classical and fractional Fokker–Planck equations, and consequently proving uniform-in-time convergence with respect to the approximation parameter. In contrast, the long-time behavior of non-confining equations is still poorly understood. I will also discuss some results and ongoing work with José Cañizo and Stéphane Mischler (Paris Dauphine), where we extend some of the previous idea to this more challenging unconfined setting.

• 📅 jueves 11 de diciembre -- 13:00
• 📍 Aula A25, Facultad de Ciencias
• 👤Conferenciante: Javier Peñafiel (ICMAT)
• 📖 Título: Topology of weak solutions in fluid mechanics
• 📄 Resumen: In this talk we will explore the role of topology in low-regularity fields describing fluids and plasmas. First, I will show that, unlike classical solutions, weak solutions of the steady Euler equations can have any prescribed topology. This is achieved by means of a novel convex integration scheme that preserves the topology of the field throughout the process. As an application, this provides counterexamples in a weak sense to Grad's conjecture on the axisymmetry of certain plasma equilibria. In the second part of the talk, I will discuss the construction of dissipative solutions of ideal MHD with nonzero helicity. Using a new approach that better respects the topology of the equations, we provide the first example of Hölder continuous solutions in which one quantity is dissipated while another is conserved, even in the absence of symmetry.