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.**

## Regla de las fases de Gibbs para potenciales Hölder en la familia de Manneville-Pomeau.

RESUMEN: En esta charla daremos una clasificación de los potenciales Hölder para las dinámicas en la familia de Manneville-Pomeau. Esta clasificación depende de la propiedades termodinámicas de los potenciales. Mostraremos que cuando existen potenciales con transiciones de fase hay dos fases en el espacio de potenciales, cada fase es un abierto conexo, y la unión de estas dos fases es densa. También mostraremos que estas dos fases tienen una frontera común y que esta frontera es homeomorfa a un subespacio de codimensión 1.

## Estudio Comparativo De La Evaluación Antropogénica Y Geogénica De La Concentración De Metales Pesados Y Lábiles En Sedimentos Marinos Superficiales Y Suelos De La Zona Norte De Chile.

Resumen: La investigación, permite la identificación, priorización, jerarquización y evaluación preliminar de la contaminación en zonas muy degradadas ambientalmente y posibilita la determinación de los niveles de los cuales se establecen los límites de inocuidad y peligrosidad en ambientes costeros. El propósito del estudio es elaborar un diagnóstico regional de los suelos y sedimentos marinos del borde costero del norte de Chile con potencial presencia de elementos trazas y metales pesados. El estudio, analiza la potencial...

## Attention is Turing Complete.

Abstract: Alternatives to recurrent neural networks, in particular, architectures based on self-attention, are gaining momentum for processing input sequences. In spite of their relevance, the computational properties of such networks have not yet been fully explored. We study the computational power of the Transformer, one of the most paradigmatic architectures exemplifying self-attention. We show that the Transformer with hard-attention is Turing complete exclusively based on their capacity to compute and access internal dense...

## Prophet Inequalities Require Only a Constant Number of Samples.

Abstract: In a prophet inequality problem, n independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as a reward. We evaluate a stopping rule by the worst-case ratio between its expected reward and the expectation of the maximum variable. Because of its connections with resource allocation and posted-price mechanisms, this problem has been intensively studied, and several variants have been introduced. While most of the literature assumes that...

## On Wu’s Inequality and the Poisson-Föllmer Process.

Resumen: In the discrete setting the Poisson distribution is a ubiquitous object, as the Gaussian distribution is in the Euclidean setting. In spite of that, it does not satisfy Gross’ log-Sobolev inequality. Nevertheless, Bobkov and Ledoux were able to prove that it satisfies a “modified” version of it, which was subsequently reinforced by Wu. In the first part of this talk we will exhibit a new stochastic proof of Wu’s modified log-Sobolev, via an entropy-minimizing process constructed by Klartag and Lehec, which we call the...

## Coarse Graph Theory I – The Questions

Resumen: Coarse graph theory is concerned with the large-scale geometric properties of infinite graphs, especially the properties preserved by quasi-isometries. Although such inquiries have been raised since the 80’s, it was usually in the context of Cayley graphs and geometric group theory. Recently the topic migrated to graph theory with intriguing outcomes. Eventually, the field of coarse graph theory was officially inaugurated and systematically treated in a paper by Georgakopoulos and Papasoglu. In this talk, I will explain...

## Aggregating opinions — do we need (Kolmogorov) complexity?

Abstract: Imagine a group of people that need each day to make some collective decision (for the entire group), choosing one of two options A and B. Some people prefer A, some prefer B, and others are OK with any of the two options. (The next day the preferences may change arbitrarily, and a new group choice is made.) The group management needs to choose A or B, in both cases making some people unhappy. This cannot be avoided completely (if someone wants A and someone else wants B, one of them will be unhappy), so the goal is more modest:...

## A spectral proof of Szemerédi’s regularity lemma.

Resumen: In this talk I will present the spectral proof of the regularity lemma due to Frieze and Kannan in the version popularized by Tao.

## Algebraic intersections in translation surface.

RESUMEN: The purpose of this talk is to discuss the maximal possible (algebraic) intersection of closed curves of a given length on translation surfaces. One way to quantify this is to define the so-called “interaction strength” of the surface. The (moduli) space of translation surfaces comes with a natural SL(2,ℝ)-action and we are interested in understanding the behaviour of the interaction stength under this action. After having introduced translation surfaces and the SL(2,ℝ)-action, we will give a few geometric ideas and focus...