Noticias en español
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.
On fraudulent stochastic algorithms.
Resumen: We introduce and analyse the almost sure convergence of a stochastic algorithm for the global minimisation of smooth functions. This diffusion process is called fraudulent because it requires the knowledge of minimal value of the function. Nevertheless, its investigation is not without interest, since in particular it appears as the limit behaviour of non-fraudulent and time-inhomogeneous swarm mean-field algorithms for global optimisation or in stochastic gradient descent algorithms in over-parametrised deep learning applications....
The 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)....
Planning 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...
The 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 $\delta > 4/5$.
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.
Quenched limits for sub-ballistic random walks in random conductances: high and low dimensions.
Resumen: Consider a random walk amongst elliptic conductances with a deterministic directional bias. For all dimensions larger or equal than 2, Fribergh proved that the walk is ballistic if and only if the mean of a conductance is finite. In the infinite mean case, under proper regularity conditions, Fribergh and Kious showed the convergence of the rescaled process towards Fractional Kinetics, in the annealed setting. I will explain how to obtain a quenched limit by exploiting a celebrated idea of Bolthausen and Sznitman. I will highlight...
Asymptotic behavior and rigidity in one-phase free boundary problems.
Abstract: In this talk, we will present some results concerning the behavior of solutions to the one-phase Bernoulli problem that are modeled –either at infinitesimal or at large scales–by one-homogeneous solutions with isolated singularity. We address the uniqueness of blow-up and blow-down limits provided that the one homogeneous solution has additional symmetries (integrability through rotations), and establish a rigidity type theorem, in the spirit of Simon-Solomon, given suitable conditions on the linearized operator around...
Optimal d-Clique Decompositions for Hypergraphs.
Abstract: We determine the optimal constant for the Erdős-Pyber theorem on hypergraphs. Namely, we prove that every n-vertex d-uniform hypergraph H can be written as the union of a family F of complete d-partite hypergraphs such that every vertex of H belongs to at most (n choose d)/(n lg n) graphs in F. This improves on results of Csirmaz, Ligeti, and Tardos (2014), and answers an old question of Chung, Erdős, and Spencer (1983). Our proofs yield several algorithmic consequences, such as an O(n lg n) algorithm to find large balanced...
Random burning of the Euclidean lattice.
Resumen: The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit speed along the edges of the graph. In joint work with Alice Contat, following Mitsche, Prałat and Roshanbin, we consider two natural random burning procedures in the discrete Euclidean torus $\mathbb{T}_n^d$, in which the points that we set on fire at each step are random variables. Our main...
The Ramsey Number of Multiple Copies of a Graph
Abstract: Let H be a graph without isolated vertices. The Ramsey Number r(nH) is the minimum N such that every coloring of the edges of the complete graph on N vertices with red and blue contains n pairwise vertex-disjoint monochromatic copies of H of the same color. In 1975, Burr, Erdős and Spencer established that r(nH) is a linear function of n for large enough n. In 1987, Burr proved a superexponential upper bound for when the long-term linear behavior starts. In 2023, Bucic and Sudakov showed that the long-term linear behavior starts...
