José Luis León Medina

José Luis León Medina

CONACYT Postdoctoral Researcher

CIMAT-Mérida


I am a postdoctoral researcher working on algebraic topology under the supervision of José Cantarero at CIMAT Mérida. My current research centers on describing the homotopical properties of some complements of hyperplane arrangements.

Previously, I got my Ph. D. from the CINVESTAV research center under the supervision of Jesús González where I worked on the topological complexity of no-$k$-equal spaces, a kind of generalization of configuration spaces.

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Interests
  • Algebraic Topology
  • Homotopy Theory
  • Topological Complexity
  • Discrete Morse Theory
Education

  • PhD in Mathematics, 2022

    CINVESTAV

  • MSc in Mathematics, 2018

    CINVESTAV

  • BSc in Mathematics, 2016

    Meritorious Autonomous University of Puebla

Experience

 
 
 
 
 
UPIITA-IPN
Mathematics Professor
UPIITA-IPN
Feb 2020 – Jan 2022 Mexico

Courses taught:

  • Linear Algebra, Probability (Fall 2021)
  • Linear Algebra, Probability, Calculus, Vector Calculus, Differential Equations (Spring 2021)
  • Numerical Analysis, Calculus, Probability and Statistics for engineering, Introduction to Complex Analysis (Fall 2020)
  • Linear Algebra, Probability, Numerical Analysis (Spring 2020)

Featured Publications

Jesús González, José Luis León-Medina
April, 2022 Journal of Homotopy and Related Structures
On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds
On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds

We compute the Lusternik-Schnirelmann category and all the higher topological complexities of non-$k$-equal manifolds $M_d^{(k)}(n)$ for certain values of $d$, $k$ and $n$. This includes instances where $M_d^{(k)}(n)$ is known to be rationally non-formal. The key ingredient in our computations is the knowledge of the cohomology ring $H^*(M_d^{(k)}(n))$ as described by Dobrinskaya and Turchin. A fine tuning comes from the use of obstruction theory techniques. The table shown above shows the Lusternik-Schnirelmann category values for the case $d=2$ and small values of $k$ and $n$.
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Publications

Jesús González, José Luis León-Medina (2022). On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds. Journal of Homotopy and Related Structures.

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Jesús González, José Luis León-Medina, Christopher Roque-Márquez (2021). Linear motion planning with controlled collisions and pure planar braids. Homology, Homotopy and Applications.

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Jorge Aguilar-Guzmán, Jesús González, José Luis León-Medina (2020). Homotopy type of skeleta of the flag complex over a finite vector space and generalized Galois numbers. Journal of Applied and Computational Topology.

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Recent Talks

Non-$k$-equal spaces [in spanish]
Se abordará el concepto de complejidad topológica y en particular examinaremos este invariante para el caso de los espacios de no $k$ …
Mar 29, 2023 10:00 AM — 11:00 AM Facultad de Matemáticas, UADY
PDF
Non-$k$-equal spaces [in spanish]

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