Noticias en español
Central 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...
Read MoreDeterministic and stochastic fixed-point iterations in normed spaces.
Abstract: In this talk, we present a survey of techniques and results on error bounds and convergence rates for both deterministic and stochastic fixed-point iterations, with a focus on methods such as the Krasnoselskii-Mann and Halpern iterations. Our primary emphasis is on general normed spaces, where we employ tools from optimal transport to derive tight error bounds. For spaces with additional structure, such as Hilbert spaces, we also discuss existing techniques and the sharp results established in the literature. Finally, we highlight applications of these findings in reinforcement...
Read MoreSome dynamical invariants under strong orbit equivalence.
Abstract: A dynamical system is usually made up of a state space and a rule (a map acting on the space) that tells us how the system evolves over time. One of the central questions in studying these systems is figuring out when two of them are essentially the same, or conjugate, as we usually say. There are several known features, called invariants, that stay the same under conjugacy, but so far, no single invariant can completely characterize when two systems are conjugate. Because of that, it is natural to look at a slightly weaker idea of equivalence, called strong orbit equivalence. All...
Read More