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.
Optimization and Economic Equilibrium.
Abstract: In the standard theory of economic equilibrium, various “agents” optimize what they want to buy and sell in order to adjust their holdings on the basis of given prices and associated budget constraints. Their decisions depend on preference relations that are representable nonuniquely by utility functions on the space of goods vectors. The standard question posed by economists is whether prices exist under which the resulting total demands of the agents are matched by total supplies. Equilibrium is a state in which, at...
From Combinatorial Optimization to Combinatorial Generation.
Abstract: We propose a new simple general approach for combinatorial generation. Given some binary strings X⊆{0,1}ⁿ, our approach consists of greedily computing a Hamilton path in a polytope with X as vertices, namely conv(X). Our main result shows that this approach works for all X⊆{0,1}ⁿ and is efficient whenever optimization over X can be efficiently solved, showing an unexplored relation between combinatorial optimization and generation. More specifically, if we can solve certain linear optimization problems for X in time O(T), we can...
Existence and stability of steady states of Flat Vlasov Poisson with a central mass density.
Abstract: El Sistema de Vlasov-Poisson Plano es usado para modelar objetos astronómicos extremadamente planos, a través de la evolución de una distribución de partículas en el plano de fase, las cuales autointeractúan a través del campo gravitacional inducido por ellas mismas. En este trabajo se estudia la construcción de estados estacionarios del Sistema de Vlasov-Poisson Plano en presencia de un potencial gravitacional externo, inducido por una densidad de masa fija. La construcción de dichos estados se realiza a través de la minimización...
Presión al infinito en shifts de Markov con alfabeto numerable.
RESUMEN: El principio variacional para la presión dice que la presión topológica es igual a el supremo de la presión de medidas invariantes. En analogía al principio variacional, definimos la presión al infinito, como el supremo de la presión de una sucesión de medidas que converge cero. En esta charla, hablaré de la presión al infinito para shifts de Markov numerables y potenciales uniformemente continuos. Discutiré algunas ideas generales y aplicaciones a la existencia de estados de equilibrio, medidas maximizantes y a resultados de gap...
The Hamilton Compression of Highly Symmetric Graphs.
Abstract: The relationship between symmetry and Hamiltonicity in graphs has gained much attention in recent years but is still not so well understood, this can be seen, for example, in the colliding conjectures of Lovász and Babai. To try to shed some light on this relationship, we introduce a measure of how symmetric the Hamilton cycles in a graph can be. We say that a Hamilton cycle C=x_1,…,x_n in a graph is k-symmetric, if the mapping x_i to x_(i+n/k) for all i=1,…,n, where indices are considered modulo n, is an automorphism of...
Constant-depth sorting networks.
Abstract: Assume that you want to sort n integers, and you have many copies of a device that can sort k integers. At one step, you can partition n integers into sets of size at most k by putting them into your devices. How many such steps do you need to sort your initial array? When k = 2, this problem is just a problem of constructing a sorting network. It can be solved in O(log n) steps, though the construction is complicated and impractical. We consider a reversed setting. Namely, we fix a number of steps and seek for the minimal k such...
The Wasserstein-Martingale projection of a Brownian motion given initial and terminal marginals.
Abstract: In one of its dynamic formulations, the optimal transport problem asks to determine the stochastic process that interpolates between given initial and terminal marginals and is as close as possible to the constant-speed particle. Typically, the answer to this question is a stochastic process with constant-speed trajectories. We explore the analogue problem in the setting of martingales, and ask: what is the martingale that interpolates between given initial and terminal marginals and is as close as possible to the constant...
Recent developments in Fourier interpolation theory.
Abstract: In this talk we will discuss some problems related to the notion of Fourier interpolation: formulas where one can recover functions from its values over a certain discrete set, and the values of its Fourier transform over a dual discrete set. These formulas arrive naturally in many situations, and we will mention a few related to certain kinds of uncertainty principles, and the theory of sphere packing.
Plataforma Agrícola Satelital PLAS: Información satelital para el manejo eficiente del riego.
Resumen: El monitoreo de la agricultura por medio de imágenes satelitales y su disponibilidad para consulta en plataformas públicas online, permiten operativizar los marcos conceptuales tradicionales para el manejo eficiente del riego. La Plataforma Agrícola Satelital – PLAS es un sistema de consulta online, que permite obtener información actualizada del nivel de desarrollo de los cultivos y estimar su consumo hídrico. La alta resolución espacial y temporal de las imágenes de los satélites Sentinel 2A y 2B (píxeles de 10 metros y 10...
Qualitative Properties for a class of fully nonlinear elliptic equations.
Abstract: In joint work with F. Pacella, we study the existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci’s extremal operators in dimension two and higher. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover, for the (negative) Pucci P^- operator, we show the existence of a critical exponent and give bounds for it. The same technique is then applied in higher dimensions to improve the...
