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.
On the Price of Anarchy for Flows over Time
Abstract: Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. In order to describe the temporal evolution of such systems one has to consider the propagation of flow across the network by tracking the position of each particle along time. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this talk I will discuss dynamic equilibria in the...
A VARIATIONAL APPROACH TO SECOND-ORDER OPTIMALITY
ABSTRATC: Conditions associated with local optimality, whether necessary or sufficient, have traditionally been approached through techniques of generalized differentiation. On the first-order level, this has been a long-standing success, although serious challenges remain for equilibrium constraints and the like. On the second-order level, a difficulty areses with the complex concepts of generalized second derivatives and the sometimes-inadequate calculus for determining them. In fact, sufficient second-order conditions of a practical...
Strongly interacting kink-antikink pairs for scalar fields on a line
Abstract: I will present a recent joint work with Michał Kowalczyk and Andrew Lawrie. A nonlinear wave equation with a double-well potential in 1+1 dimension admits stationary solutions called kinks and antikinks, which are minimal energy solutions connecting the two minima of the potential. We study solutions whose energy is equal to twice the energy of a kink, which is the threshold energy for a formation of a kink-antikink pair. We prove that, up to translations in space and time, there is exactly one kink-antikink pair having this...
Robust Revenue Maximization Under Minimal Statistical Information
Abstract: We study the problem of multi-dimensional revenue maximization when selling $m$ items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we assume that the seller has a very restricted knowledge of this prior: they only know the mean $\mu_j$ and an upper bound $\sigma_j$ on the standard deviation of each item’s marginal distribution. Our goal is to design mechanisms that achieve good revenue against an ideal optimal auction that has...
Aplicaciones de la teoría de forzamiento para los homeomorfismos del anillo compacto
ABSTRACT En esta charla presentaremos una introducción a la teoría de forzamiento de trayectorias transversas para homeomorfismos de superficie. Usando esta teoría, estudiamos los conjuntos de rotación de los homeomorfismos del anillo compacto que son isotópicos a la identidad. Probamos que si un tal homeomorfismo preserva el área, entonces todo número en su conjunto de rotación es realizado por un conjunto compacto e invariante. Trabajo con Fábio Tal.
On the Cycle Augmentation Problem: Hardness and Approximation Algorithms.
Abstract: In the k-Connectivity Augmentation Problem we are given a k-edge-connected graph and a set of additional edges called links. Our goal is to find a set of links of minimum cardinality whose addition to the graph makes it (k+1)-edge-connected. There is an approximation preserving reduction from the mentioned problem to the case k=1 (a.k.a. the Tree Augmentation Problem or TAP) or k=2 (a.k.a. the Cactus Augmentation Problem or CacAP). While several better-than-2 approximation algorithms are known for TAP, nothing better is known for...
Lower bounds on the Hausdorff dimension of the Rauzy gasket
ABSTRACT: The Rauzy gasket is an important fractal object arising in several dynamical constructions, such as Novikov’s problem and some renormalization schemes for certain families of interval exchange maps. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension D of the Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed the upper bound D<2. In this talk, I will explain how to use the thermodynamical results of Cao, Pesin and Zhao to show that D > 1.19....
REPLICATOR DYNAMICS: OLD AND NEW
Abstract: We introduce the unilateral version associated to the replicator dynamics and describe its connection to on-line learning procedures, in particular tomultiplicative weight algorithm. We show the interest of handling simultaneously discrete and continuous time analysis. We then survey recent results on extensions of this dynamics: regularization function and variable weights. This includes no regret algorithms, time average and link to best reply dynamics in two person games, application to equilibria and variational inequalities,...
Problemas clásicos en EDO desde un punto de vista no autónomo
ABSTRACT: En esta charla daremos a conocer las versiones no autónomas de los clásicos problemas de estabilidad global y linealización suave. Además haremos un link entre el problema de estabilidad global autónomo y la conjetura jacobiana.
Estabilización de una clase de ciclos heterodimensionales
ABSTRACT : Un difeomorfismo f tiene un ciclo (heterodimensional) si existen conjuntos hiperbólicos (transitivos) de índices diferentes (dimensión del fibrado inestable) cuyas variedades invariantes se intersectan cíclicamente. El ciclo de f es Cr-robusto si toda pequeña Cr-perturbación de f tiene un ciclo asociado a las continuaciones de estos conjuntos hiperbólicos. Si el ciclo de f es definido por un par de sillas hiperbólicas decimos que este ciclo puede ser Cr-estabilizado si toda Cr-vecindad de f contiene difeomorfismos con un ciclo...
