CV
Porfirio Leandro León Álvarez
Contact
Facultad de Ciencias
UNAM (National Autonomous University of México)
porfirio.leon@ im.unam.mx
Education
Ph.D. in Mathematical Sciences, National Autonomous University of México
Science Faculty
- Thesis: Classifying spaces for discrete groups for the family of virtually abelian subgroups.
- Advisor: Dr. Luis Jorge Sánchez Saldaña
- Defense: April 2024
Master in Mathematical Sciences, National Autonomous University of México
Institute of Mathematics Cuernavaca
- Dissertation: The Eilenberg-Ganea theorem for families
- Director: Dr. Luis Jorge Sánchez Saldaña
- Defense: December 6, 2019
- General exams approved: Differential Geometry, Differential Topology, and Algebra
Bachelor of Mathematics, Autonomous University of Guerrero, Faculty of Mathematics
- Thesis: Classification of Compact Surfaces
- Director: Dr. Rita Jiménez Rolland
- Defense: October 19, 2016
Articles and Projects in Progress
(with Rita Jiménez Rolland ). On the virtually cyclic dimension of normally poly-free groups. Submitted (2023) Arxiv.
Classifying spaces for families of abelian subgroups of braid groups, RAAGs and graphs of abelian groups. Porfirio L. León Álvarez, Accepted for publication in the Glasgow Mathematical Journal 2024:1-18. DOI:10.1017/S0017089523000496
(with Luis Jorge Sánchez Saldaña and Rita Jiménez Rolland ). Commensurators of abelian subgroups and the virtually abelian dimension of mapping class groups. Journal of Pure and Applied Algebra, 228(6):107566, 2024.
(with Luis Jorge Sánchez Saldaña ). Classifying spaces for the family of virtually abelian subgroups of orientable 3-manifold groups. Forum Math. 34 (2022), no. 5, 1277–1296. Arxiv .
Training of Human Resources
- Member of the thesis committee of a student from the Faculty of Sciences, UNAM: Diego Leipen Lara. Thesis defense date: May 2023
Organized Seminars
- Member of the organizing committee of the Student Seminar, at the Institute of Mathematics Cuernavaca unit, National Autonomous University of Mexico (join with Jesús Hernández Serda and Sergio Gutiérrez) from 2018 to 2019. Cuernavaca, Morelos, México
- Member of the organizing committee of the Characteristic Classes Seminar, Institute of Mathematics, National Autonomous University of México (join with Karegar Baneh Kohal, Quentin) from August 2019 to November 2019. Cuernavaca, Morelos, México
Teaching
- Assistant in the Introduction to the Geometry Group theory course. At the Faculty of Sciences of UNAM with Dr. Luis Jorge Sánchez Saldaña in the semesters 2024-1.
- Assistant in the course of algebraic topology II. At the Institute of Mathematics, UNAM, C.U. Unit with Dr. Luis Jorge Sánchez Saldaña in the semester 2024-1.
- Assistant in the basic course of algebraic topology. At the Institute of Mathematics, UNAM, C.U. Unit with Dr. Luis Jorge Sánchez Saldaña in the semesters 2022-2 and 2023-2.
- Assistant in the Topology II course. At the Faculty of Sciences of UNAM with Dr. Luis Jorge Sánchez Saldaña in the semesters 2022-1 and 2021-1.
- Assistant in the Topology III course. At the Faculty of Sciences of UNAM with Dr. Luis Jorge Sánchez Saldaña in the semester 2021-2.
- Assistant in the Modern Algebra I course. At the Faculty of Sciences of UNAM with Dr. Luis Jorge Sánchez Saldaña in the semester 2020-2.
Talks in Seminars and Conferences
By Invitation
- Virtually abelian dimension of graphs of groups. At the Geometry, Topology, and Dynamics Meeting, June 16, 2023, Morelia Michoacán, México
- An introduction to classifying spaces for families, Oaxaca Geometry, Topology and Algebra Seminar (GATO), May 25, 2023
- Virtually abelian dimension of 3-manifold groups, at the CIMAT-UADY Topology Meeting from October 4 to 6, 2022, Mérida, Yucatán, México
By Request
- Commensurators of abelian subgroups and the virtually abelian dimension of mapping class groups, Prospects in Topology Seminar at the Center for Mathematical Sciences, Morelia, Michoacán, June 12, 2023
- Virtually abelian dimension of mapping class groups, Student Seminar, Institute of Mathematics C.U. Unit, UNAM, 2023
- Virtually cyclic dimension of the mapping class group of a non-orientable surface, 55th National Congress of the Mexican Mathematical Society, University Center of Exact Sciences and Engineering at the University of Guadalajara, 2022
- Virtually abelian dimension of 3-manifold groups, at "The 39th Annual (Online) Workshop in Geometric Topology" (https://faculty.tcu.edu/gfriedman/GTW2022/), 2022
- Coxeter groups and the Eilenberg-Ganea Conjecture, Student Seminar, Institute of Mathematics Cuernavaca Unit, UNAM, 2019
- Geometric and cohomological dimension for families of subgroups, Student Seminar, Institute of Mathematics, UNAM, C.U, 2019
- The Eilenberg-Ganea theorem, Student Seminar, The Center for Research in Mathematics, A.C, 2018
- The Eilenberg-Ganea theorem, 51st National Congress of the Mexican Mathematical Society, Villahermosa, Tabasco, 2018
- Definition and examples of $K_{0}(R)$ 1, Topology Seminar, Institute of Mathematics Cuernavaca Unit, UNAM, 2017
- Definition and examples of $K_{0}(R)$ 11, Topology Seminar, Institute of Mathematics Cuernavaca Unit, UNAM, 2017
Languages
- Spanish, Native.
- English, Intermediate level.
References
- Dra. Rita Jiménez Rolland, Universidad Nacional Autónoma de México, Instituto de Matemáticas unidad Oaxaca, México, rita@im.unam.mx
- Dr. Luis Jorge Sánchez Saldaña, Universidad Nacional Autónoma de México, Facultad de Ciencias, México, luisjorge@ciencias.unam.mx