Noticias en español
Recent advances on multiple ergodic averages
RESUMEN In 1977, Furstenberg gave a dynamical proof of the theorem of Szemerédi on the existence of arithmetic progressions in dense subsets of integers. In doing so, he initiated the use of ergodic methods to solve problems originating from additive combinatorics and number theory. A central object of study in this field are multiple ergodic averages, a class of multilinear operators that generalize classical Birkhoff averages and can be used to count the number of arithmetic patterns in dense sets of integers. In this talk, I will outline the history of multiple ergodic averages, with...
Read MoreSingle orbits and Wiener-Wintner theorem
RESUMEN A single-orbit approach to dynamics links the global properties of a dynamical system with the behaviour of its orbits. During the talk, I shall discuss what can be deduced about the system from the existence of an orbit satisfying the conclusion of the Wiener-Wintner theorem (a Wiener-Wintner generic orbit). I will examine the spectrum of ergodic measures by examining the behaviour of their Wiener–Wintner generic points. Moreover, by investigating the properties of a “regular” subclass of such points, I shall characterise ergodic measures with discrete...
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 MorePlanning Deeply Decarbonized Power Systems
Abstract: The energy transition is reshaping power system planning and operation as renewable penetration increases and electrification expands into sectors such as heating and cooling, making systems more dependent on weather-driven variability and uncertainty. Addressing these challenges requires models that can capture both short-term operational flexibility and long-term uncertainty, supported by suitable solution methods. This presentation examines the challenges of long-term power system planning under uncertainty in the context of the energy transition and explores the use of...
Read MoreThe Brown-Erdős-Sós conjecture in dense triple systems.
Abstract: In 1973, Brown, Erdős, and Sós conjectured, in an equivalent form, that for any $\delta > 0$ and integer $e \geq 3$, every sufficiently large linear 3-uniform hypergraph with at least $\delta n^2$ edges contains a collection of $e$ edges whose union spans at least $e+3$ vertices. In this talk, we show a proof of the conjecture for the case $\delta > 4/5$.
Read MoreThe rightmost particle of the inherited sterility contact process.
Resumen: The contact process with inherited sterility provides a probabilistic framework for studying population control strategies inspired by the Sterile Insect Technique. In this model, an infected particle can create a fertile infected particle (with probability p) or a sterile infected particle (with probability 1-p) which will behave like an “environment” blocking the propagation of the infection. The main challenge is that this model is not attractive (since an increase of fertile individuals potentially causes that of sterile ones). Sonia Velasco previously proved that this process...
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