Online CIMPA Pre-School El Salvador 2020
Streaming channel
https://www.youtube.com/watch?v=1jj6AwdBChU
Algebraic Methods in Topology
Online CIMPA Pre-School “Algebraic Methods in Topology”, December 14-19, 2020. This Pre-School consists in 4 online mini-courses covering foundational topics in Algebra and Topology as preparation for the CIMPA School “Algebraic Methods in Topology” to be held in El Salvador in 2022. This Pre-School is aimed for senior-undergraduate and graduate math students. The deadline to register for this Pre-School is November 30, 2020. Acceptance will be notified at a later date. The official languages are English and Spanish. Online CIMPA Pre-School activities: Opening talk (Language: Spanish). Online mini-courses (Platform: Google Meet):
- Foundations of Homotopy Theory (Language: Spanish).
- Introduction to Abelian Groups and Modules (Language: Spanish).
- An introduction to Stable Homotopy Theory (Language: Spanish).
- Foundations of Module Theory (Language: English).
Support
Courses
Foundations of Homotopy Theory
By Ingrid Martínez, Universidad de El Salvador.
Language: Spanish.
El minicurso de fundamentos de homotopía se desarrollará en tres sesiones donde se abordarán conceptos y resultados importantes de la teoría de homotopía:
Sesión 1: Homotopía de funciones y grupo fundamental. H- espacios, espacios lazo y suspensiones.
Sesión 2: Construcción de espacios: Cilindros y Conos. Grupos de homotopía y sucesiones de homotopía.
Sesión 3: Propiedades de extensión y levantamiento de homotopía.
Material: here.
Bibliography: Algebraic Topology from Homotopical Viewpoint; Aguilar M., Gliter S. & Prieto C.
Introduction to Abelian Groups and Modules
By Gabriel Chicas, Universidad de El Salvador.
Language: Spanish.
En este minicurso abordaremos elementos básicos de la teoría de grupos abelianos y módulos. Nos enfocaremos en algunos problemas de clasificación: el de módulos finitamente generados sobre un dominio de ideales principales, y más generalmente sobre un dominio de Dedekind. Concluiremos con una discusión acerca de módulos proyectivos sobre un dominio de Dedekind.
Material: here.
Bibliography: Abstract Algebra, 3rd; Dummit and Foote. A Course in Homological Algebra, 2nd; Hilton and Stammbach.
An introduction to Stable Homotopy Theory
By Omar Antolín, Universidad Nacional Autónoma de México.
Language: Spanish.
Los espectros son una manera concreta de representar teorías de cohomología generalizadas en términos de espacios topológicos y tienen una peculiar naturaleza dual, topológica y algebraica. En este mini-curso daremos una introducción a la teoría de homotopía estable, que es la rama de la topología encargada de estudiar a los espectros. Hablaremos de los teoremas de la teoría de homotopía que son precursores de la teoría estable, de las definiciones de espectros y algunos ejemplos clave, y de cómo su estudio es una generalización del álgebra.
Foundations of Module Theory
By Sean Sather-Wagstaff, Clemson University.
Language: English.
One way to understand a geometric object is to understand its symmetries. This idea translates powerfully to numerous areas of mathematics. In algebra, one way this manifests is through the study of modules: one understands a ring (for instance, arising in geometry or number theory) by understanding the objects it influences. (Maybe think of this like the discovery of Pluto, which was first inferred by astronomers observing *something* affecting other celestial bodies.) In this mini-course, we will present foundational material about rings and modules, in preparation for the follow-up course “Foundations of homological algebra applied to modules.”
Bibliography: Abstract Algebra; Dummit and Foote. Algebra; Hungerford.
Opening talk
By CIMPA representative Jorge Mozo, Universidad de Valladolid.
Language: Spanish and English.
Schedule
December 14 – 19, 2020
Time zone: UTC-6
| M | T | W | T | F | S | |
|---|---|---|---|---|---|---|
| 09:00 – 10:30 | Course 1 | Course 1 | Course 1 | Course 3 | Course 3 | Course 3 |
| 10:45 – 11:45 | Discussion session Course 1 |
Discussion session Course 1 |
Discussion session Course 1 |
Discussion session Course 3 |
Discussion session Course 3 |
Discussion session Course 3 |
| 12:00 – 13:00 | Opening talk | |||||
| 14:00 – 15:30 | Course 2 | Course 2 | Course 2 | Course 4 | Course 4 | Course 4 |
| 15:45 – 16:45 | Discussion session Course 2 |
Discussion session Course 2 |
Discussion session Course 2 |
Discussion session Course 4 |
Discussion session Course 4 |
Discussion session Course 4 |
Online mini-courses (Platform: Zoom):
- Foundations of Homotopy Theory (Language: Spanish).
- Introduction to Abelian Groups and Modules (Language: Spanish).
- An introduction to Stable Homotopy Theory (Language: Spanish).
- Foundations of Module Theory (Language: English).
Organization
Local Organizing Committee
- Dr. Riquelmi Cardona
- Dr. Nerys Funes
- Licda. Cecilia Martínez
- M.Sc. Ingrid Martínez
- Dr. Aarón Ramírez
- Dr. Dimas Tejada
Scientific Committee
- Dr. Manuel Cruz López (Universidad de Guanajuato)
- Dr. Francisco Javier Gallego (Universidad Complutense de Madrid)
- Dr. Nadia Romero (Universidad de Guanajuato)
- Dr. José Seade (Universidad Nacional Autónoma de México)
- Dr. Alejandra Trujillo (Centro de Investigación en Matemáticas A.C.)
Local Coordinator
- Dr. Aarón Ramírez
External Coordinator
- Dr. Begoña Vitoriano
CIMPA Representative
- Dr. Jorge Mozo
Registration
This Online CIMPA Pre-School Algebraic Methods in Topology School is mainly dedicated to senior-undergraduate and graduate math students interested in Algebra, Topology, or Geometry, from El Salvador and neighboring countries. Other students/researchers may apply as well.
All participants are required to fill out the registration form.
The deadline to register is November 30, 2020; acceptance will be notified at a later date. Participation is completely free of charges.
If you have any registration problem you can write to info@ecimpasv2020.org