Noticias en español
Distribution Modulo 1 and Applications
Abstract: In this work, we present an overview of fundamental results in the theory of uniform distribution modulo 1 and the closely related field of discrepancy theory. After introducing the main concepts, tools, and classical theorems, we explore how these ideas can be applied to problems arising in dynamical systems and fractal analysis. In particular, we discuss their role in understanding the spectral properties of substitution dynamical systems and in the study of Bernoulli convolutions.
Read MoreThe Haagerup property.
Abstract: The Haagerup property is an analytic property of groups that generalises amenability. It originated from the study of C*-algebras, and it has found applications in several areas of mathematics, including harmonic analysis, geometric group theory, topology, and ergodic theory. This talk will consist in an introduction to this property and its connections to group actions on Banach spaces.
Read MoreCentral limit theorems for strcutured branching processes
Abstract: Branching processes are mathematical models for populations that evolve by random reproduction: each individual lives for some time and then gives birth to new individuals, whose lives and offspring evolve independently. When such systems are enriched with spatial or structural information—allowing individuals to move, interact, or carry traits—they form infinite-dimensional stochastic processes that capture a wide range of phenomena, from cell division to particle systems. In this talk, I will discuss recent results on the central limit theorem (CLT) for a large class of such...
Read MoreSecretary Problems and Combinatorial Optimal Stopping.
Abstract: Secretary problems constitute a classical setting of online decision-making, where discrete elements arrive in uniformly random order, reveal their weight, and must be accepted or rejected irrevocably, with the aim of maximizing a given function over the selected set. In the most general form of the problem, we are given a combinatorial feasibility constraint (e.g. a matroid) and the selected set has to be feasible with respect to that constraint. In such problems, the objective is to design algorithms which guarantee a multiplicative factor approximation with respect to the...
Read MoreTwo-Edge Connectivity via Pac-Man Gluing.
Abstract: We study the 2-edge-connected spanning subgraph (2-ECSS) problem: Given a graph $G$, compute a connected subgraph $H$ of $G$ with the minimum number of edges such that $H$ is spanning, i.e., $V(H) = V(G)$, and $H$ is 2-edge-connected, i.e., $H$ remains connected upon the deletion of any single edge, if such an $H$ exists. The $2$-ECSS problem is known to be NP-hard. In this work, we provide a polynomial-time $(\frac 5 4 + \varepsilon)$-approximation for the problem for an arbitrarily small $\varepsilon>0$, improving the previous best approximation ratio of...
Read MoreInverse and reverse optimization problems.
Abstract: nverse and reverse optimization problems aim to adjust the objective function of an underlying optimization problem while minimizing the extent of modification. In inverse optimization, the goal is to modify the objective function so that a given feasible solution becomes optimal. In reverse optimization, the goal is to modify the objective function so that the optimum value attains a specified number. In this talk, we mainly focus on inverse maximum-capacity optimization problems under the bottleneck Hamming distance, the weighted infinity norm and weighted span objectives. Our...
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