René I. García-Lara

Mérida

México

I am a postdoctoral research at National Autonomous University of Mexico, where I work on differential geometry and mathematical physics applied to a variety of problems. Details can be found on my publications page. I keep notes of the topics I find interesting, these are freely available at the following links:

I am also an enthusiast of computer science and entrepenurship, specially regarding the art of solving data related problems for the industry, links to some of my projects can be found here.

I try to keep up to date my media presence, but time has proved me this is a NP task, if you are curious about any of the topics I work in, in the academia or elsewhere, please contact me by social media (links at the bottom of the page) or drop me a line

news

Nov 16, 2025	XX UADY's Geometry Coloquium
Feb 23, 2025	Geometry of SOL-type groups seminar
Jan 9, 2025	The volume of the moduli space of rotational vortex systems seminar
Nov 11, 2024	XIX UADY's Geometry Coloquium
Aug 29, 2023	Seminar-Type Workshop on Topological Solitons

selected publications

Existence of Abelian BPS Vortices on Surfaces with Neumann Boundary Conditions

Rene Garcia-Lara

Mathematical Physics, Analysis and Geometry, 2025

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Existence of abelian BPS vortices on a manifold with boundary satisfying Neumann boundary conditions is proved. Numerical solutions are constructed on the Euclidean disk, and the L2-metric of the moduli space of one vortex located at the interior of a rotationally symmetric disk is studied. The results presented extend previous work of Manton and Zhao on quotients of surfaces that admit a reflection.
@article{GarciaLara2025ExistenceOA, title = {Existence of Abelian BPS Vortices on Surfaces with Neumann Boundary Conditions}, author = {Garcia-Lara, Rene}, journal = {Mathematical Physics, Analysis and Geometry}, year = {2025}, volume = {28}, doi = {10.1007/s11040-025-09533-z}, url = {https://doi.org/10.1007/s11040-025-09533-z}, }
The Geometry of the Space of Vortices on a Two-Sphere in the Bradlow Limit

R. I. Garcı́a Lara, and J. M. Speight

Communications in Mathematical Physics, Sep 2023

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It is proved that the normalized L2 metric on the moduli space of n-vortices on a two-sphere, endowed with any Riemannian metric, converges uniformly in the Bradlow limit to the Fubini–Study metric. This establishes, in a rigorous setting, a longstanding informal conjecture of Baptista and Manton.
@article{Lara_2023, doi = {10.1007/s00220-023-04842-2}, url = {https://doi.org/10.1007%2Fs00220-023-04842-2}, year = {2023}, month = sep, publisher = {Springer Science and Business Media {LLC}}, author = {Lara, R. I. Garc{\'{\i}}a and Speight, J. M.}, title = {The Geometry of the Space of Vortices on a Two-Sphere in the Bradlow Limit}, journal = {Communications in Mathematical Physics}, }
A Family of Complex Kleinian Split Solvable Groups

Waldemar Barrera, Rene Garcia, and Juan Pablo Navarrete

Bulletin of the Brazilian Mathematical Society, New Series, Dec 2022

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In this article, using techniques of Lie groups and dynamical systems, it is shown that lattices of a family of split solvable subgroups of PSL(N+1,C) are complex Kleinian. Also, it is shown that there exists a minimal limit set for the action of these lattices on the complex projective space and that there are exactly two maximal discontinuity regions.
@article{Barrera2022, author = {Barrera, Waldemar and Garcia, Rene and Navarrete, Juan Pablo}, title = {A Family of Complex Kleinian Split Solvable Groups}, journal = {Bulletin of the Brazilian Mathematical Society, New Series}, year = {2022}, month = dec, day = {01}, volume = {53}, number = {4}, pages = {1277-1289}, issn = {1678-7714}, doi = {10.1007/s00574-022-00303-x}, url = {https://doi.org/10.1007/s00574-022-00303-x}, }