Carlos Barrera-Rodriguez, PhD
UC Davis 2012



Some of my interests
  • Curve Complex, Pants Complex, Marking Complex
  • Hierarchies
  • Hyperbolic Manifolds/Geometry
  • Low-dimensional Topology
  • Geometric Group Theory
  • Dynamics
  • Heegaard Splittings 
  • Kleinian Groups
  • (Non-)Filling Curves
  • Train Tracks
  • Foliations/Laminations

“Many people have an impression, based on years of schooling, that mathematics is an austere and formal subject concerned with complicated and ultimately confusing rules”. “Good mathematics is quite opposite to this. Mathematics is an art of human understanding. … Mathematics sings when we feel it in our whole brain.”
                                                                                  - W.P. Thurston, 2009





About me
 
    I am a mexican (mostly independent) mathematician. I have been in the following places as student and/or instructor: Universidad Autónoma Metropolitana at Iztapalapa (UAM), Centro de Investigación en Matemáticas (CIMAT) and the University of California Davis (UCD) from which I recently graduated under the supervision of Joel Hass. The title of my thesis project was A collection of multi-curve complexes, where I defined a new complex extending the notion of disjointness in the curve complex, by a more convenient notion, namely, non-fillingness.

I am interested in Geometric Topology and Applied Math. The topics I am 
currently interested in are multi-curve complexes, Teichmueller spaces, Heegaard splittings, hyperbolic manifolds, dynamics and random walks. Since I graduated I do research on a collection of multi-curve complexes of a surface. These complexes, somehow, interpolate  the Curve Complex and the Pants Complex. I am still investigating the coarse geometry of these new complexes in these days and, I guess, I will do this for a while.

I just finished working as postdoctoral researcher at the Instituto de Matemáticas (UNAM) in the beautiful/cultural/magic Oaxaca city. I have started working  on a personal (math-based) project in the industry, which actually I already started developing some years ago. This project possesses several branches and sub-branches of development, some of them with major priorities right now. 

I did research on Biomath as undergrad and still I feel interested in doing  applications from the point of view of the Geometry. I am also interested in Sci Computing, looking foward to interact with this soon.

You can obtain a copy of my CV, teaching statement or other info you are interested in by request, just click here and I will answer your message as soon as I read it.


I am part of the UNAM committee building the UNAM-based program: Oaxaca Project for Education

This project is coming to life in 2017, as projected.