2025-03-06
14:00hrs.

Seminario Fismat
Piotr M. Hajac. Mathematical Institute of The Polish Academy of Sciences
Tba
Sala 1 - Facultad de Matemáticas

2025-01-21
11:00hrs.

Seminario de Análisis y Geometría
Tomás Sanz Perela. Universitat de Barcelona
Stable cones in the Alt-Phillips free boundary problem
Abstract:

Sala 1

2025-01-16
17:10hrs.

Seminario de Análisis y Geometría
Ederson Moreira Dos Santos. Universidade de São Paulo (São Carlos)
Standing waves for nonlinear Hartree type equations: existence and qualitative properties
Abstract:
In this talk I will report some results on standing wave solutions for nonlinear Hartree type equations, regarding existence and some qualitative properties, such as definite sign, radial symmetry and sharp asymptotic decay.  
Joint work with with Eduardo Böer (ICMC-USP).
Sala multiuso primer piso Edificio Villanueva

2025-01-16
16:00hrs.

Inverse Problems and Control Theory. 
Eric Bonnetier. Institut Fourier, Université Grenoble-Alpes
Uniform estimates for small volume asymptotics
Abstract:
We revisit the problem of  studying the impact of a perturbation of the coefficients of an elliptic PDE on a set of small size. We show that the asymptotic structure of the perturbed solution can be described in terms of the spectrum of the Poincaré variational operators defined by the perturbations. This approach turns out to be useful in obtaining estimates which are uniform in the coefficient contrast.
Sala de Seminarios Felipe Álvarez, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile. https://eventos.cmm.uchile.cl/seminarioipct/

2025-01-16
16:10hrs.

Seminario de Análisis y Geometría
Dennis Kriventsov. Department of Mathematics, Rutgers University
Rectifiability of interfaces with positive Alt-Caffarelli-Friedman limit via quantitative stability
Abstract:
The Alt-Caffarelli-Friedman (ACF) monotonicity formula captures fine behavior of pairs of nonnegative harmonic functions which vanish on the mutual boundary of complementary domains. I will describe the following theorem: the set of points with positive limit for the ACF formula, corresponding roughly to where both functions have linear growth away from the interface, is countably (n-1)-rectifiable. The proof leverages a new quantitative stability property for the ACF formula, which in turn is based on a new quantitative stability result for the Faber-Krahn inequality. Indeed, we show that the square of the L^{^2} distance between the first Dirichlet eigenfunctions of some domain and some ball of the same volume is controlled by the difference of their first eigenvalues. Our proof of this relies on regularity theory for some “critical" modifications of Bernoulli-type free boundary problems. This is based on joint work with Mark Allen and Robin Neumayer.
Sala multiuso primer piso Edificio Villanueva

2025-01-15
13:30hrs.

Seminario de Ingeniería Matemática y Computacional
Fabián Flores Bazán. Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción
Convexidad en optimización cuadrática no convexa, y más allá
Abstract:
Convexidad es una condición que muchos matemáticos quisieran que el problema que enfrentan lo cumpla. Por otro lado, existen resultados en Análisis Funcional, Cálculo de Variaciones, Pencil de Matrices, Inclusiones Diferenciales, entre otras áreas de la Matemática, las cuales muestran que la convexidad surge de modo natural, ya sea de modo directo o indirectamente. Algunos de aquellos resultados se presentaran con énfasis en el mundo cuadrático; también veremos las consecuencias que traen consigo, particularmente en Optimización Matemática cuando se estudia la validez de la propiedad de dualidad fuerte.
Presencial en Auditorio Edificio San Agustín

2025-01-13
16:30hrs.

Seminario de Sistemas Dinámicos
Cristina Lizana. Universidade Federal Da Bahia
Intrinsic ergodicity for a certain class of Derived from Anosov
Abstract:
We will talk briefly about some classic examples of Derived from Anosov (DA), that is, homotopic maps to an Anosov diffeomorphism, whose dynamics are partially hyperbolic. We will address some known results related to entropy invariance and the existence (and uniqueness) of measures of maximal entropy for this class of diffeomorphisms. Finally, we will present recent results in collaboration with L. Parra (PUCV) and C. Vásquez (PUCV) for a certain class of DA generated after a Hopf bifurcation, previously introduced by [M. Carvalho'93].
Sala 1

2025-01-09
16:10hrs.

Seminario de Análisis y Geometría
Luciano Sciaraffia. Albert-Ludwigs-Universität Freiburg
Minimal networks and curvature flow singularities
Abstract:
The object of our study is networks, that is, unions of a finite number of curves. The talk will address two topics: the existence of certain minimal configurations and the curvature flow.
I will begin by reviewing some of the literature on minimal networks on surfaces, with particular emphasis on the case of the 2-sphere. Inspired by a conjecture of Hass and Morgan regarding the existence of theta-shaped minimal networks in convex 2-spheres, I will then consider such networks on spheres of any dimension, endowed with a Riemannian metric close to the standard one. Using a finite-dimensional reduction method in conjunction with the Lusternik–Schnirelmann category, we establish results on existence and multiplicity.
Next, I will introduce the network flow and review some of its key properties, focusing on the formation of singularities and the main differences from the shortening flow of simple curves. I will discuss the so-called type-0 singularities, after which it is possible to extend the flow. In the specific case of symmetric initial data with two triple junctions, we show that the set of singular times is finite.
The methods employed in the main proofs are elementary, and the talk should be accessible to master's students with a background in analysis. 
Sala 1