Noticias en español
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.
Read MoreThe 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 MoreVariable 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 using constant parameters, and thus share the same...
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 MoreParametric 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 cuts that give the GMI closure for any polyhedra in...
Read MoreMathematical 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 identify some of the difficulties and present the...
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