Noticimat 26

Seminarios

Seminario de Probabilidad  

Lunes 08

Hora:  12:45 (CDMX)

Ponente: Samuel Johnston

Título: Continuous Kasteleyn theory and beads on the torus

Lugar: Salón de seminarios

Resumen: We develop a continuous version of Kasteleyn theory to study the bead model on the torus. These are the point processes on the semi-discrete torus Tn := [0, 1)×{0, 1, . . . , n−1} (thought of as n unit length strings wrapped around a doughnut) with the property that between every two consecutive points on same string, there lies a point on the neighbouring strings. We obtain an explicit formula for the volume of bead configurations with n strings and k beads per string. The asymptotics of this formula verify a recent conjecture of Shlyakhtenko and Tao (2020). in the setting of free probability. We study the correlation functions of the process, expanding on the work of Boutillier (2009). Various limits of our process recover certain Markov chains, and we show that TASEP on the ring may be constructed as an exponential change of measure of the noncolliding walkers of Gordenko (2020).

Web del seminario: https://www.cimat.mx/~jagil/Seminarios/Seminarios/Seminarios_2022.html

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Coloquio CIMAT – DEMAT  

Miércoles 10

Hora:  12:00 (CDMX)

Ponentes: Raúl Rojas González (Freie Universität Berlin), Francisco Sánchez Sánchez, Adolfo Sánchez Valenzuela (CIMAT), con la colaboración de Rafael Gamboa Hirales (ITAM)

Título: Métodos de Representación Proporcional para una Reforma Política en México

Enlace de Transmisión: https://us06web.zoom.us/j/81161632128?pwd=S0w4Y1lhendPNUxrUVpiejlkdllGdz09 

Resumen: Desde hace tiempo se anunció que habría una reforma a la ley electoral que eliminaría las llamadas diputaciones plurinominales y que convertiría las diputaciones de los 300 distritos electorales existentes en diputaciones de representación proporcional. En esta charla queremos presentar las ideas básicas que hay detrás de los métodos y algoritmos más populares para asignar diputados de representación proporcional y presentar también algunos cálculos basados en estos diferentes métodos que sugieren que es mejor no eliminar la figura de las diputaciones plurinominales a fin de garantizar una representatividad de los partidos mucho más cercana a la proporción de votos obtenidos en las elecciones. Usamos los resultados de las elecciones del 2021 como laboratorio para probar los diferentes métodos y darnos cuenta de que no se requerirían más de unas cuantas diputaciones adicionales (entre 12 y 50 dependiendo del modelo) para conseguir que la representatividad de cada partido se acerque mucho a la proporcionalidad de los votos recibidos.

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Seminario de Computación  

Miércoles 10

Hora:  12:30 (CDMX)

Ponente: Dr. Victor Zavala (University of Wisconsin-Madison)

Título: Graph-Structured Optimization: Properties, Algorithms, and Software

Enlace de Transmisión: https://bluejeans.com/810722229

Resumen: We study properties for nonlinear optimization problems whose structures are induced by graphs. These problems arise in many applications such as dynamic optimization, optimal control, stochastic optimization, optimization with partial differential equations, and network optimization. We show that for a given pair of nodes, the sensitivity of the primal-dual solution at one node against a data perturbation at the other node decays exponentially with respect to the distance between these two nodes on the graph. In other words, the solution sensitivity decays exponentially as one moves away from the perturbation point. We discuss how this property provides new and interesting insights on the behavior of complex systems and how it enables the design of new decomposition and approximation algorithms and software. Specifically, we discuss model predictive control formulations with specialized time discretization approaches and overlapping Schwarz decomposition approaches for solving large-scale problems. We also show how to easily implement graph-structured problems in the Julia programming language.

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Seminario de Topología en Dimensiones Bajas “Fico González Acuña”

Jueves 11

Hora:  11:00 (CDMX)

Ponente: John Luecke (The University of Texas at Austin)

Título: Fibered Simple Knots

Resumen: A simple knot is a knot in a lens space built from the union of a pair of properly embedded arcs, one in each of a pair of standard meridianal disks. We prove that a simple knot in the lens space L(p,q) fibers if and only if its order in homology does not divide any remainder occurring in the Euclidean algorithm applied to the pair (p,q). One corollary is that if p=m2 is a perfect square, then any simple knot of order m fibers, answering a question of Cebanu. More generally, we compute in a similar way the leading coefficient of the Alexander polynomial of a simple knot. This is joint work with Josh Greene.

Web del seminario: http://www.fico-ldtseminar.org

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