Publications

2023

1. 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

   Abs Bib

   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}
   }

2022

1. 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

   Abs Bib

   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}
   }

2. Smooth knot limit sets of the complex hyperbolic plane

   Waldemar Barrera, Rene Garcia, and Juan Pablo Navarrete

   Boletín de la Sociedad Matemática Mexicana, Jul 2022

   Abs Bib

   It is shown that if a regular knot of class }}C^2}}is embedded in the boundary of the complex hyperbolic plane as the limit set of a discrete subgroup of }}\backslashmathrm {PU} (2,1)}}, then it is either a chain or an }}\backslashmathbb {R}}}-circle.

   @article{Barrera2022Knots,
     author = {Barrera, Waldemar and Garcia, Rene and Navarrete, Juan Pablo},
     title = {Smooth knot limit sets of the complex hyperbolic plane},
     journal = {Bolet{\'i}n de la Sociedad Matem{\'a}tica Mexicana},
     year = {2022},
     month = jul,
     day = {16},
     volume = {28},
     number = {3},
     pages = {58},
     issn = {2296-4495},
     doi = {10.1007/s40590-022-00451-6},
     url = {https://doi.org/10.1007/s40590-022-00451-6}
   }

2021

1. Geometric models of soliton vortex dynamics

   Rene Garcia

   School of mathematics, University of Leeds, Jul 2021

   Bib

   @phdthesis{rene:thesis:2020,
     author = {Garcia, Rene},
     title = {Geometric models of soliton vortex dynamics},
     school = {School of mathematics, University of Leeds},
     year = {2021},
     address = {Leeds, UK}
   }

2019

1. Chains Homotopy in the Complement of a Knot in the Sphere S3

   W Barrera, A Cano, Rene Garcia, and 1 more author

   Bulletin of the Brazilian Mathematical Society, New Series, Jul 2019

   Bib

   @article{barrera2019chains,
     title = {Chains Homotopy in the Complement of a Knot in the Sphere  S3},
     author = {Barrera, W and Cano, A and Garcia, Rene and Navarrete, JP},
     journal = {Bulletin of the Brazilian Mathematical Society, New Series},
     volume = {50},
     number = {4},
     pages = {971--997},
     year = {2019},
     publisher = {Springer Berlin Heidelberg}
   }

2. Geometry of AdSn

   Rene Garcia

   In Avanza IX: Workshop on Kleinian groups and related topics, Jul 2019

   Bib

   @inproceedings{adsnGeometry,
     author = {Garcia, Rene},
     title = {Geometry of {AdSn}},
     booktitle = {Avanza {IX}: Workshop on Kleinian groups and related topics},
     year = {2019},
     address = {Autonomous University of Ciudad Juarez, Ciudad Juarez, Mexico}
   }

2018

1. Three-dimensional Sol manifolds and complex Kleinian groups

   Waldemar Barrera Vargas, Rene Garcia, and Juan Navarrete Carrillo

   Pacific Journal of Mathematics, Jul 2018

   Bib

   @article{barrera2018three,
     title = {Three-dimensional Sol manifolds and complex Kleinian groups},
     author = {Barrera Vargas, Waldemar and Garcia, Rene and Navarrete Carrillo, Juan},
     journal = {Pacific Journal of Mathematics},
     volume = {294},
     number = {1},
     pages = {1--18},
     year = {2018},
     publisher = {Mathematical Sciences Publishers}
   }