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.
Tail bounds for detection times in mobile hyperbolic graphs.
Abstract: Motivated by Krioukov et al.’s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a dynamic model of hyperbolic graphs in which vertices are allowed to move according to a Brownian motion maintaining the distribution of vertices in hyperbolic space invariant. For different parameters of the speed of angular and radial motion, we analyze tail bounds for detection times of a fixed target and obtain a complete...
Finite point blowup for the critical generalized Korteweg-de Vries equation.
Abstract: In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de~Vries (gKdV) equation, including the determination of sufficient conditions for blowup,the stability of blowup in a refined topology and the classification of minimal mass blowup. Exotic blow-up solutions with a continuum of blow-up rates and multi-point blow-up solutions were also constructed. However, all these results, as well as numerical simulations, involve the bubbling of a solitary...
Nash Flows over Time: Uniqueness, Continuity and Long-term behavior.
Abstract: In the talk, we consider a dynamic model of traffic that has received a lot of attention in the past few years, Nash Flows over time. Users control infinitesimal flow particles aiming to travel from a source to destination as quickly as possible. Flow patterns vary over time, and congestion effects are modeled via queues, which form whenever the inflow into a link exceeds its capacity. We will see that assuming constant inflow into the network at the source, equilibria always settle down into a “steady state” in which...
Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons.
Abstract: We consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth...
A simple model for an epidemic with contact tracing and cluster isolation, and a detection paradox.
Abstract: We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation, which is inspired by a recent work of Bansaye, Gu and Yuan. Notably, we compute explicitly the asymptotic proportion of isolated clusters with a given size amongst all isolated clusters, conditionally on survival of the epidemic. Somewhat surprisingly, the latter differs from the distribution of the size of a typical cluster at the time of its detection; and we explain the reasons behind this...
A 2-Approximation for the Bounded Treewidth Sparsest Cut Problem in FPT Time.
Abstract: Abstract: In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut over the total demand of the crossing edges of D. In this work, we study the non-uniform sparsest cut problem for supply graphs with bounded treewidth k. For this case, Gupta, Talwar and Witmer [STOC 2013] obtained a 2-approximation with polynomial running time for fixed k, and the...
Continuity for maximal operators at the derivative level.
Abstract: Maximal operators are central objects in harmonic analysis. The oscillatory behavior of such objects has been an important topic of study over the last decades. However, even in the dimension one there are interesting questions that remain open. In this talk we will discuss recent developments and open questions about this topic, particularly about the boundedness and continuity for such operators at the derivative level.
The fibering method applied to the level sets of a family of functionals.
Abstract: Given an one-parameter family of C1-functionals, Φμ : X →R, defined on an uniformly convex Banach space X, we describe a method that permit us find critical points of Φμ at some energy level c ∈ R. In fact, we show the existence of a sequence μ(n,c), n ∈N, such that Φμ(n,c) has a critical level at c ∈ R, for all n ∈ N. Moreover, we show some good properties of the curves μ(n,c), with respect to c (for example, they are Lipschitz), and as a consequence of this analysis, we recover many know results on the literature concerning...
Quantum Decoherence for probabilists.
Resumen: Quantum decoherence (QD) is today one cornerstone in the development of quantum computing (QC). This refers to the collapse of a quantum state into a classical one. From a mathematical point of view, its modelling has also been a major problem, motivating the development of new research in open systems theory. One could classify today this phenomenon at the interface between non-commutative and commutative probabilities. The general question is: how a quantum evolution becomes classical? Is this inevitable? Shall QC live with that?...
Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization.
Abstract: We investigate quasi equilibrium problems in a reflexive Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered (Joint work with Monica Bianchi and Gabor...
