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.
Buscando ciclos balanceados.
Resumen: El teorema de los patrones inevitables dice que, para n suficientemente grande, toda 2-coloración de E(K_n) con “suficientes” aristas en cada clase cromática contiene al menos uno de dos patrones: una K_2t donde una clase cromática induce una K_t o bien una K_2t donde una clase cromática induce dos K_t disjuntas. Una gráfica G es balanceable si existe un entero no negativo k tal que toda 2-coloración de E(K_n) con más de k aristas en cada clase cromática contiene una copia de G de forma balanceada (la mitad de sus...
Scattering via Morawetz estimates for the non-radial inhomogeneous nonlinear Schr ̈odinger equation.
Abstract: The concentration-compactness-rigidity method, pioneered by Kenig and Merle, has become standard in the study of global well-posedness and scattering in the context of dispersive and wave equations. Albeit powerful, it requires building some heavy machinery in order to obtain the desired space-time bounds. In this talk, we present a simpler method, based on Tao’s scattering criterion and on Dodson-Murphy’s Virial/Morawetz inequalities, first proved for the 3d cubic nonlinear Schr ̈odinger (NLS) equation. Tao’s criterion is, in some...
Some discrete optimization problems in matching markets.
Abstract: In the classical stable marriage problem, we are given two sets of agents – students and schools – with each student and school having a total order of agents from the opposite set. The goal is to form disjoint pairs of students and schools so that the resulting matching satisfies a fairness property known as stability. In their fundamental work, Gale and Shapley showed that a stable matching always exists and gave a fast algorithm to find one. These strong structural and algorithmic results propelled the application of...
Potencias de caminos en torneos.
Resumen: En esta charla se presentaran tres resultados recientes acerca de k-potencias de caminos en torneos, con un esquema de su demostración, así como la idea de “k-absorbers”, que es clave en esta, en particular: -Todo torneo contiene k-potencias de caminos lineales. -Todo torneo epsilon-intransitivo contiene k-potencias de ciclos lineales. -Todo torneo puede descomponerse como la unión de 2^c k-potencias de caminos
Wave-Structure interactions: oscillating water columns in shallow water.
Abstract: Wave energy converters (WECs) are devices that convert the energy associated with a moving ocean wave into electrical energy. In this talk we present a mathematical model of a particular wave energy converter, the so-called oscillating water columns in shallow water regime. This model can be reformulated as two transmission problems: one is related to the wave motion over the stepped topography and the other one is related to the wave-structure interaction where a fixed partially immersed structure is installed. We analyze the...
Non-intersecting paths in the plane, loop-erased walks and random matrices.
Resumen: Non-intersecting processes in one dimension have long been an integral part of random matrix theory, at least since the pioneering work of F. Dyson in the 1960s. For planar (two-dimensional) state space processes, it is not clear how to generalize these connections since the paths under consideration are allowed to have self-intersections (or loops). In this talk, we address this problem and consider systems of random walks in planar graphs constrained to a certain type of non-intersection involving their loop-erased parts (this is...
Stability in Matrix Games.
Abstract: We consider the simplest game, Matrix Games, and basic stability questions on the value and strategies upon perturbations on the payoff matrix. Considering polynomial perturbations, we design polynomial-time algorithms for the following tasks: (a) ensuring that, for every sufficiently small error, there is a strategy to guarantee that the value is at least the value of the error-free case; (b) ensuring that there is a fixed strategy to guarantee that, for every sufficiently small error, the value is at least the value of the...
Grafos expansivos e inmersiones.
Resumen: En esta charla seguiremos estudiando el uso de grafos expansivos en problemas extremales. Se estudiará cómo utilizar expansión para encontrar inmersiones de grafos completos en grafos con condiciones de grado promedio.
Separation and Interaction energy between domain walls in a nonlocal model.
Abstract: We analyse a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter epsilon > 0. The model gives rise to transition layers, called Néel walls, and we study their behaviour in the limit epsilon -> 0. The analysis has some similarity to the theory of Ginzburg-Landau vortices. In particular, it gives rise to a renormalised energy that determines the interaction (attraction or repulsion) between Néel walls to leading order. But while Ginzburg-Landau vortices show...
