Noticimat 27

Título: Bienvenida

Hora: 12:30 pm

(Trasmisión por el sistema bluejeans: https://bluejeans.com/463972286).

Resumen: A modo de una cordial bienvenida a todos los nuevos integrantes de la comunidad CIMAT-DEMAT, se presentará un panorama del área de Ciencias de la Computación y se explicará la estructura y las líneas de conocimiento de su Maestría en Ciencias de la Computación. Además habrá intervenciones de algunas otras áreas del Centro con las cuales se han tenido colaboraciones habitualmente.

Estudiantes de nuevo ingreso de la maestría en Ciencias de la Computación del CIMAT y de la Licenciatura en Computación Matemática de DEMAT, están especialmente invitados. Esperamos contar con su participación.

 

Ponente: Marcos Jardim (IMECC/UNICAMP, Brasil)

Título: Classification of codimension one distributions of degree two on the projective space

Hora: 3:30 pm

(Trasmisión por el sistema bluejeans: https://bluejeans.com/759804451).

Resumen: In this talk I will provide a complete classification of codimension one distributions of degree 2 on the three dimensional projective space, generalizing the classification of codimension one foliations of degree 2 given by Cerveau and Lins Neto. We describe all possible singular schemes and tangent sheaves of such distributions and speculate on the topological and algebraic properties of integrability.

 

Ponente: Jesús de Loera (University of California, Davis)

Título: A CW-complex of Monotone Polyhedral Paths: Geometric/topological meditations about the performance of the Simplex Method

Hora: 10:00 am

(Trasmisión por el sistema bluejeans: https://bluejeans.com/401449328).

Resumen: George Dantzig’s Simplex method is a work horse of modern computational mathematics. Because linear programs (LPs) appear in all areas of application the Simplex methods was elected as one of the top 10 algorithms in the 20th century. Surprisingly, despite its popularity and almost 80 years of research we still do not fully understand its complexity and behavior.

To bound the number of iterations of the Simplex method we take a geometric point of view and investigate the possible lengths of monotone paths inside the oriented graphs of polyhedra (oriented by the objective function). We are interested in both the shortest and the longest monotone paths possible and estimate the (monotone) diameter and the height of some famous combinatorial polyhedra (such as TSP, fractional matching polytopes, and others). But how far apart are two monotone paths of an LP? E.g., if I use two pivot rules the Simplex method traces two paths, is there a notion of distance between them? As we look at all monotone paths together we see a metric space structure which can be used to count how many are there or to generate them randomly. This comes from a very natural graph (the flip-path graph) and CW complex structures (cellular-strings complex) on the set of monotone paths These objects are important in topological combinatorics (Baues complexes and polyhedral subdivisions studied by Billera, Sturmfels, Gelfand, Kapranov, Zelevinsky and others in the early 1990’s) and in discrete optimization (In particular the complexity of the simplex method with work going back to Klee). In my talk I will discuss some natural counting problems associated with the discrete geometric situation. Our main enumerative results include bounds on the number of monotone paths, and on the the diameter of the space of monotone paths (how far are two monotone paths from each other?). The picture is fairly complete in dimension three, but plenty of open problems remain for high dimensional polytopes.

The new theorems presented in my talk come from three recent papers (in Arxiv), the first joint work with Moise Blanchard (MIT) and Quentin Louveaux (U. Liege) the second joint work with Christos Athanasiadis (U. Athens) and Zhenyang Zhang (UC Davis), the third with Sean Kafer (U. Waterloo) and Laura Sanita (Eidhoven U).

Felicitamos a los siguientes alumnos:

 

Erick Salvador Álvarez Valencia, quien ovtuvo el grado de Maestro en Ciencias con Especialidad en Computación y Matemáticas Industriales el pasado miécoles 12, con la presentación y defensa de su tesis Métodos de Deep Learning Aplicados a Colorización Automática de Imágenes y Transferencia de Estilos. En el jurado participaron el Dr. Johan Jozef Lode Van Horebeek (CIMAT), presidente; el Dr. Iván Cruz Aceves (CIMAT), secretario; y el Dr. Óscar Susano Dalmau Cedeño (CIMAT), vocal y director de la tesis.

 

Fernando Saldaña García, quien este viernes 14 obrtuvo el grado de Doctor en Ciencias con Orientación en Matemáticas Aplicadas, con la presentación y defensa de su tesis titulada Mathematical Modeling Approaches in Epidemiology: Within Host-Dynamics, Control Strategies and Cost-Effectiveness Analysis. El jurado estuvo integrado por el Dr. Marcos Aurelio Capistrán Ocampo (CIMAT), presidente; el Dr. Jorge Xicoténcatl Velasco Hernández (UNAM), secretario; el Dr. José Geiser Villavicencio Pulido (UAM), vocal; el Dr. Fernando Alarid Escudero (CIDE), vocal; y el Dr. José Ignacio Barradas Bribiesca (CIMAT), vocal y director de la tesis.