Noticias en español
Non-linear stability of hyperbolic collisionless many-particle systems.
Abstract: I will present upcoming non-linear stability results concerning the asymptotic behavior of solutions to classical models arising in kinetic theory. First, I will present an asymptotic stability result for the exterior of the Schwarzschild family of black holes as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. We exploit the normal hyperbolicity of the trapped set in the black hole exterior to obtain decay in time of the energy momentum tensor. I will also speak about an asymptotic stability result for small data solutions to the...
Read More¿Qué hacen las educadoras de párvulos para enseñar matemáticas? Un análisis de las tareas, estrategias e interacciones.
RESUMEN Las habilidades matemáticas tempranas juegan un rol importante en el desempeño escolar de niñas, niños y jóvenes, ya que marcan diferencias en el ritmo y nivel de aprendizaje. En esta presentación se mostrarán los resultados de una investigación doctoral que tuvo por objetivo caracterizar las prácticas de enseñanza de las educadoras de párvulos en momentos de instrucción matemática. A través de un enfoque metodológico mixto, se estudiaron las tareas matemáticas, las estrategias e interacciones que las educadoras despliegan, así como los factores que se relacionan con...
Read MoreProblem Decomposition in Convex Optimization: Advances Beyond ADMM.
Abstract: Applications of convex optimization in areas like image processing and machine learning have stimulated a huge interest in solution methodology that can take advantage of underlying decomposable structure in a problem, especially when iterations can make good use of “prox” mappings on the problem’s components. Very popular in this development has been the Alternating Direction Method of Multipliers (ADMM). But other approaches that branch out from the same mathematical roots in different modes now offer new advances in the flexibility of problem formulation and...
Read MoreEl grupo de automorfismos de los grafos de fichas de los bipartitos completos.
Abstract: Sea $G$ una gráfica simple de $n$ vértices y $k$ un entero tal que $1\leq k\leq n-1$. El grafo de $k$-fichas, $F_k(G)$, de $G$ es el grafo cuyos vértices son los $k$-conjuntos de vértices de $G$, y donde dos de estos $k$-conjuntos son adyacentes si su diferencia simétrica es una arista de $G$. En esta plática hablaremos sobre la relación que existe entre los grupos de automorfismos de $G$ y de $F_k(G)$. Además, daremos un bosquejo de la prueba para determinar el grupo de automorfismos de $F_k(K_{m,n})$, donde $K_{m,n}$ denota al grafo bipartito completo. En esta familia de grafos...
Read MoreLifting Apportionment Methods to Weighted Fair Division.
Abstract: We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. This setting (known as weighted fair division) constitutes a generalization of the well-studied apportionment problem, and we present two approaches for lifting apportionment methods to weighted fair division. In the first part of the talk, we focus on additive valuations and show that picking sequences derived from divisor methods provide natural envy-freeness,...
Read MoreOn the duality between height functions and continuous spin systems.
Abstract: We revisit the well known duality relation between integer valued height functions and spin systems with O(2) symmetry. We will apply some simple corollaries from this duality to transfer information from one model to the other. First, we deduce a type of Gaussian domination for the height-function variance. Second, we deduce the monotonicity of this variance with respect to a natural temperature parameter. Finally, we show how “delocalisation” of planar height functions implies a so-called BKT phase transition in the dual (planar) spin...
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