Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as **Spanish Only.**

## Asymptotic stability manifolds for solitons in the generalized Good Boussinesq equation.

Abstract: In this talk, I shall consider the generalized Good-Boussinesq model in one dimension, with power nonlinearity and data in the energy space $H^1\times L^2$. I will present in more detail the long-time behavior of zero-speed solitary waves, or standing waves. By using virial identities, in the spirit of Kowalczyk, Martel, and Muñoz, we construct and characterize a manifold of even-odd initial data around the standing wave for which there is asymptotic stability in the energy space.

## Un abordaje regional al estudio de la propagación y control del COVID-19 en Chile.

Resumen: Esta charla se centra en un trabajo desarrollado en el marco de mi tesis doctoral, donde pretendo compartirles algunas particularidades presentes en la evolución del virus SARS-Cov2 en las regiones de Chile, en especial para el periodo contemplado entre el 3 marzo al 27 de julio de 2020, teniendo en cuenta las medidas de cuarentena aplicadas a nivel regional antes del Plan Paso a Paso, y que intentamos involucrar en la formulación y descripción de nuestro modelo compartimental, el cual ajustamos a datos regionales para estimar...

## A new proof of Aldous-Broder theorem.

Resumen: The Aldous–Broder algorithm is a famous algorithm used to sample a uniform spanning tree of any finite connected graph G, but it is more general: it states that given a reversible M Markov chain on G started at r and up to the cover time, the tree rooted at r formed by the steps of successive first entrance in each node (different from the root) has a probability proportional to the product of these edges according to M, where the edges are directed toward r. In this talk I will present an extension to the non-reversible case and a...

## A (2 + epsilon)-approximation algorithm for preemptive weighted flow time on a single machine.

Abstract: In a recent breakthrough in scheduling, Batra, Garg, and Kumar gave the first constant approximation algorithm for minimizing the sum of weighted flow times. Wiese and I (STOC’21) managed to improve this large unspecified constant to 2 + epsilon. I will give a very graphic presentation of the algorithmic techniques behind this.

## When cultures collide: Preparing to teach mathematics to culturally diverse students.

ABSTRACT Mathematics education research has acknowledged the role of culture in teaching and learning, and specifically how mathematics classrooms create a context that legitimizes or invalidates various forms of knowledge. Mathematics teacher educators (MTEs) have a responsibility to expose prospective teachers (PSTs) to the different ways students’ reason about and learn mathematics and teach them how to build on students’ mathematical and cultural backgrounds. This preparation must help PSTs recognize their own cultural socialization and...

## Invariant Family of Leaf measures and The Ledrappier-Young Property for Hyperbolic Equilibrium States.

ABSTRACT: Let be a Riemannian, boundaryless, and compact manifold with , let be a () diffeomorphism of , and let be a Hölder continuous potential on . We construct an invariant and absolutely continuous family of measures (with transformation relations defined by ), which sit on local unstable leaves. We present two main applications. First, given an ergodic homoclinic class , we prove that admits a local equilibrium state on if and only if is “recurrent on ” (a condition tested by counting periodic points), and one of the leaf...

## Expansión sublineal en grafos.

Resumen: En esta charla introduciremos los aspectos básicos de los grafos con expansión sublineal y su uso en problemas extremales. En particular, mostraremos una aplicación sencilla para encontrar subdivisiones del grafo completo en grafos con grado promedio relativamente bajo. Acá el link al zoom: https://uchile.zoom.us/j/83539034403?pwd=NlZ6UGwzNndpZHNZNThGSzViMldLdz09 password 624=05

## Improved Approximation Algorithms for 2-Dimensional Knapsack: Packing into Multiple L-Shapes, Spirals, and More.

In the 2-Dimensional Knapsack problem (2DK) we are given a square knapsack and a collection of n rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed non-overlappingly into the knapsack. The currently best known polynomial-time approximation factor for 2DK is 17/9+eps<1.89 and there is a (3/2+eps)-approximation algorithm if we are allowed to rotate items by 90 degrees. In this talk, I will present a (4/3+eps)-approximation algorithms in polynomial time for both cases,...

## About infinite energy solutions to the incompressible Navier-Stokes equations.

Abstract: We study estimates for the Navier–Stokes equations, in a sufficiently robust context to be applied to the construction of : 1) Discretely self-similar solutions, for initial data satisfying the weak condition to be locally square integrable. 2) Regular axially symmetrical solutions without swirl, for initial data which together with his gradient belong to a weighted Lebesgue space.

## Scheduling in the Random-Oder Model.

Abstract: We study Online Makespan Minimization, one of the most basic scheduling problems, in the random-order model. Here jobs of a given input arrive in a uniformly chosen random order as opposed to the classical adversarial model, which considers worst-case orders. The random-order model originates from the Secretary Problem and has received quite some research interest over the last years. For scheduling, the random-order model provides beyond worst-case guarantees while still not being overly pessimistic. Furthermore, it leads to a...