COLOQUIO DE MATEMÁTICAS 2020-I
ENTRADA LIBRE
Organizadores: Dario García
 
Se ofrecerá café, aromática y galletas después de las 5.00 p.m. al lado del salón del Coloquio.
Coloquios
anteriores:
Jueves 30 de Enero de 2020
B-402
4.00 p.m.
Federico Ardila - San Francisco State University
La geometría de las matroides

- Resumen


La teoría de matroides es una teoría combinatoria de la independencia, que tiene sus orígenes en el álgebra lineal y la teoría de grafos, y que resulta tener conexiones importantes con muchas otras áreas. Con el tiempo, las raíces geométricas de esta teoría se han hecho bastante más profundas, dando muchos frutos nuevos.

Recientemente, el acercamiento geométrico a la teoría de matroides ha llevado al desarrollo de matemática fascinante en la intersección de la combinatoria, el álgebra, y la geometría, y a la solucion de varias conjeturas clásicas. Esta charla resumirá algunos logros recientes.

Invitado por:

Darío Alejandro García
Jueves 13 de Febrero de 2020
B-402
4.00 p.m.
Jarod Alper - University of Washington
Advances in Moduli

- Resumen


Moduli spaces are fascinating spaces that appear in various guises across mathematics. Vaguely, a moduli space is a space (e.g. topological space, manifold or algebraic variety) whose points are in bijective correspondence with isomorphism classes of certain topological, geometric or algebraic objects (e.g. curves or vector bundles). We will provide an introduction to moduli spaces that appear in algebraic geometry with an emphasis on examples. We will see that the properties of a moduli space depend crucially on properties of the automorphism groups of the objects. We will first explain how one can construct a moduli space as a projective variety in the case when the automorphism groups are finite. Our final goal is to show how recent breakthroughs in the foundations of moduli theory allow for similar constructions even when the automorphism groups are not finite.

Invitado por:

Darío Alejandro García
Jueves 20 de Febrero de 2020
B-402
4.00 p.m.
Elio Espejo - University of Nottingham Ningbo China
A simultaneous blow-up problem arising in tumor modeling

- Resumen


Although macrophages are part of the human immune system, it has been remarkably observed in laboratory experiments that decreasing its number can slow down the tumor progression. We analyze through a recently mathematical model proposed inthe literature, necessary conditions for aggregation of tumor cells and macrophages. In order to do so, we prove the possibility of having blow-up in finite time. Next, we study if the aggregation of macrophages can occur when having a low density of tumor cells, and vice versa. With this purpose, we consider the problem of analyzing the existence or not of a simultaneous blow-up. We achieve this goal thanks to a novel process that allows us to compare the entropy functional associated with the density of each population, which turns out to be also a method to find enough conditions for having a simultaneous blow-up.

Invitado por:

Darío Alejandro García