Noticias en español
Toros exóticos y acciones de SL(d,Z).
RESUMEN: Una de las características más distintivas del toro d-dimensional (i.e. el producto de d círculos) T^d es que admite una acción C-infinito efectiva del grupo SL(d,Z) de matrices d x d con entradas enteras. Uno podría preguntarse si una acción así (o cualquier acción no trivial) también existe sobre toros exóticos, es decir, variedades diferenciables que son homeomorfas pero no difeomorfas a T^d. En mi charla, luego de revisar algunas generalidades sobre variedades exóticas, voy a discutir esta pregunta.
Read MoreLimiting distributions of Spherical and Spin O(N) models: Appearance of GFF.
Resumen: Spherical model is a mathematical model of a ferromagnet introduced by Berlin and Kac in 1952 as a rough but analytically convenient modification of the Ising model. Since its inception it has enjoyed considerable popularity among the mathematicians and physicists as an exactly soluble model exhibiting a phase transition. In this talk we will explain its relation to the Gaussian free field in the infinite volume limit and to the spin O(N) model in the infinite spin-dimensionality limit of the latter.
Read MoreHamiltonicity in pseudorandom graphs: absorbing paths.
Abstract: In this second talk, we will introduce the “extendability method” for embedding sparse structures in expander graphs and we will use it to construct efficient absorbers to solve the Hamiltonicity problem in pseudorandom graphs.
Read MoreDecaimiento de correlaciones para ciertos atractores no uniformemente hiperbólicos.
RESUMEN: Un problema clásico en sistemas dinámicos es conocido como el problema de realización, el cual consiste en preguntar si dada una variedad compacta M, uno puede construir un difeomorfismo en M con ciertas propiedades ergódicas. Vamos a estudiar el decaimiento de correlaciones para ciertos sistemas dinámicos no uniformemente hiperbólicos con respecto a su medida SRB. El sistema g que vamos a considerar se obtiene de un difeomorfismo uniformemente hiperbólico f al que se le aplica el procedimiento de desaceleración. Bajo ciertas hipótesis en f y en la vecindad donde se aplica la...
Read MoreLearning-augmented Assignment: Santa Claus does Load Balancing.
Abstract: Assignment problems are among the most well-studied in online algorithms. In these problems, a sequence of items arriving online must be assigned among a set of agents so as to optimize a given objective. This encompasses scheduling problems for minimizing makespan, p-norms, and other objectives, as well as fair division problems such as the Santa Claus problem and Nash welfare maximization. One common feature is that many of these problems are characterized by strong worst-case lower bounds in the online setting. To circumvent these impossibility results, recent research has...
Read MoreHamiltonicity in pseudorandom graphs: Pósa rotation.
Abstract: In this series of talks, we will study different approaches to the Hamiltonicity problem in sparse pseudorandom graphs. In this first talk, we will review the celebrated “extension-rotation” technique pioneered by Pósa in the 70s and how to use it in pseudorandom graphs to find Hamilton cycles.
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