Noticias en español
The Hurwitz automorphism problem and its “translation surface” versión.
Abstract: In 1893, Hurwitz showed that a compact Riemann surface of genus g ≥ 2 has at most 84(g-1) automorphisms. This bound is optimal for an infinite family of genera but there is also an infinite family of genera for which the bound is not optimal. The Hurwitz automorphism problem consists in finding the optimal bound for every genus, and apart from partial results in specific cases it is far from being solved. In this talk we will explain the first sentence of this abstract and give a geometric intuition for the result. On the way, I will discuss a similar problem for translation...
Read MoreAn Introduction to Online Matching.
Abstract: During my two-month visit to CMM, I began exploring a new direction in Online Matching. Online Matching is a typical model for decision-making under uncertainty: resources must be allocated to requests arriving sequentially in real time, without full knowledge of future demand, to maximize welfare or utility. This question arises in many settings, including ridesharing platforms, the allocation of goods and services, and (perhaps unfortunately) online advertising. Since its introduction in the 1990s by Karp, Vazirani, and Vazirani, this problem has become a benchmark in the field...
Read MoreCompartmental Models for Infectious Diseases: Structure, Intervention, and Applications.
Abstract: Compartmental models have become a fundamental tool for understanding the spread of infectious diseases and evaluating the potential impact of public health interventions. By dividing populations into epidemiological classes and describing transitions between them, these models provide a flexible mathematical framework for studying disease dynamics across a wide range of contexts. In this talk, I will present an overview of compartmental modeling for infectious diseases, including model formulation, qualitative analysis, intervention strategies, and interpretation of outcomes....
Read MoreAn orbit around quasi-trasitive graphs
Abstract: A graph is called quasi-transitive if it has finitely many orbits under automorphism. I will present some recent advances on quasi-transitive graphs, especially in the planar and minor-free cases. I will also talk about some related recent work with Agelos Georgakopoulos and Bobby Miraftab.
Read MoreDistribution 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.
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