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.
Parametric Polyhedra in Mixed-Integer Programming.
Abstract: We present some old and new results on arbitrary families of parametric polyhedra. First, if the constraint matrix is fixed, in the literature there are structural results for the integer hull and the finiteness of cutting plane closures for varying r.h.s. For instance, recently, Becu et al. proved in “Approximating the Gomory Mixed-Integer Cut Closure Using Historical Data” that the GMI closure of this family is finitely generated, in the sense that there exists a finite list of aggregation weights defining the GMI...
Variable stepsize splitting methods as relocated fixed-point iterations.
Abstract: Splitting methods exploit model structures to decompose complex optimisation problems into simpler pieces, easier to handle. A prominent instance in this family is the Douglas-Rachford algorithm, which stands out due to its simplicity and numerical stability. Traditional convergence guarantees assume constant stepsizes, while the theory with variable stepsizes is scarce, limiting the improvement of numerical performance. Including the aforementioned method, several optimisation algorithms can be recast as fixed-point iterations...
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...
Notions of openness in semigroup actions
RESUMEN We study the notion of openness of shifts transformations given by abstract semigroup actions. In 1966, Parry proved that the only one-sided subshifts with open shift map are the SFTs. In our work, we extend this theorem in several directions for some abstract semigroup actions, introducing the notion of synchronizing sets and study some applications. We will also discuss some interesting examples on N2, Q+ and free semigroups.
Mathematical Optimization Models for the Euclidean Steiner Tree Problem in R^n.
Abstract: In this talk, we review the mathematical optimization models for the Euclidean Steiner Tree Problem (ESTP) in n dimensions proposed in the literature. The development of such models for the ESTP began in the late 1990s. The ESTP is a mixed integer nonlinear optimization problem with a history dating back to the 17th century. Several properties of its optimal solutions are well known, but it is still a big challenge to encode these properties in its modeling, aiming for its numerical resolution with branch-and-bound algorithms. We...
An 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,...
An artificial intelligence method to find extremizers in classical Strichartz inequalities.
Abstract: In this talk we present a new method where machine learning provides clues for the discovery of extremizers in several unsolved Strichartz inequalities appearing in classical problems of Harmonic Analysis. This method is primarily based (but not bounded to) Physics Informed Neural Networks (PINNs), with a novel use of the minimization procedure. We provide several examples of critical points and extremizers found by this method, expecting that some of them are proved as correct solutions to the theoretical minimization problem. This...
Exact positive codegree thresholds for perfect matching.
Abstract: Rödl, Ruciński and Szemerédi found best-possible codegree conditions that force the existence of perfect matchings in $k$-graphs. Given that the codegree is too strong for many applications, we study this question for a weaker, but more versatile degree condition, which maintains the codegree’s constructive power: the positive codegree. For a $k$-graph, this corresponds to the minimum degree over all sets of size $k-1$ with degree at least one. For $k\geq 3$ , we show exact minimum positive codegree conditions for the...
Convergence Rates for Stochastic Proximal and Projection Estimators
Abstract: In this talk, we discuss explicit convergence rates for the stochastic smooth ap-proximations of infimal convolutions introduced and developed in [2, 3]. In particular,we quantify the convergence of the associated barycentric estimators toward prox-imal mappings and metric projections. We prove a dimension-explicit √δ bound, with explicit constants for the proximal mapping, in the ρ-weakly convex (possibly nonsmooth) setting, and we also obtain a dimension-explicit √δ rate for the metric projection onto an arbitrary convex set with...
The Rawlsian Prophet: Max-Min Fair Online Allocation.
Abstract: Prophet inequalities are a central framework in online stochastic decision making, comparing online algorithms to an omniscient benchmark. The utilitarian objective of maximizing expected total value is well understood, with tight competitive ratios across full-information, sample-based, and combinatorial settings. We study prophet inequalities under Rawlsian max-min fairness objectives, and distinguish between two natural notions of fairness: ex-ante and ex-post. The former aims to maximize the minimum expected value, while the...
