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.
Dispersive effective behavior of high-contrast periodic media
Abstract: I will discuss my recent work with Y. Ershova and A. Kiselev, demonstrating that spectral problems for quantum graphs with rapidly oscillating high-contrast weights are asymptotically equivalent to “homogenised” models with energy-dependent interface conditions. We show that these asymptotically equivalent models are directly related (in the sense of Schur-Frobenius duality) to models for time-dispersive media, which in the time domain involve memory, and we characterize the corresponding time convolution kernels...
The long-term behaviour of a queue-based dynamic traffic model
Abstract: The fluid queueing model, introduced by Vickrey in ’69, is probably the simplest model that plausibly captures the notion of time-varying flows. Although the model is quite simple, our current theoretical understanding of equilibrium behaviour in this model is rather limited, and many fundamental questions remain open. I will discuss the resolution of a deceptively simple-sounding problem: do queue lengths remain bounded in the equilibria under natural necessary conditions? (Joint work with Roberto Cominetti and José...
Gagliardo-Nirenberg-Sobolev inequalities in domains
Abstract: Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions. Joint work with Rafael Benguria and Cristobal...
Gagliardo-Nirenberg-Sobolev inequalities in domains
Abstract: Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions.
SUPERSET: A (super)natural variant of the card game SET
Abstract: We consider SUPERSET, a lesser-known but interesting variant of the famous card game SET. Here, players look for SUPERSETs instead of SETs, that is, the symmetric difference of two SETs that intersect in exactly one card. In this paper, we pose questions that have been previously posed for SET and provide answers to them; we also show relations between SET and SUPERSET. For the regular deck of cards, which can be identified with F_3^4, we give an elegant proof for the fact that the maximum number of cards that can be on the table...
On the 3D Ginzburg-Landau model of superconductivity
Abstract: The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the occurrence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical field. We are interested in the regime of small ɛ, where ɛ>0 is the inverse of the Ginzburg-Landau parameter. In this regime, the vortices are at main order codimension 2 topological singularities. In this talk I will present a quantitative 3D vortex...
Existence of solutions to a pure critical elliptic system in a bounded domain
Abstract: http://capde.cl/past-seminars/
Structural-based Approach to Complexity of Optimization Algorithms
Abstract: The past few decades have witnessed tremendous progress in the field of Mathematical Optimization which led to a large proliferation of new optimization methods to many scientific fields. Among these is the field of machine learning whose applicability heavily relies on solvers which are capable of efficiently solving challenging large-scale optimization problems. Notwithstanding, we still lack an adequate complexity theory which satisfactorily quantifies the computational resources required for solving optimization problems of this...
