José Javier Álvarez Pacheco

Cuernavaca Unit of the Institute of Mathematics of the National Autonomous University of Mexico, Mexico

José Javier Álvarez Pacheco is a mathematician from Costa Rica who works in representation or character varieties of surface groups.

the artwork

Salto singular

Spanish - Singular leap - 2026 - Graphite pencil on paper

audio commentary

I love the idea behind the fundamental group of a space: how the ways you can move around – in some elastic sense – gives you information about it. The study of singularities is also fascinating: understanding how and in what measure a space fails to be nice is quite intriguing and is also a somewhat natural question to ask: if something is not nice, why not? Can we make it nice by some transformation? On the thought process, it was quite natural to consider my leaving Costa Rica and starting an adventure in Mexico. Then it ocurred to me to deform the globe to connect these two places.

José Javier Álvarez Pacheco

The change in way of living and mathematical learning due to the opportunity to move to Mexico for a postgraduate program

mathematics in Costa Rican culture

Roads, houses and buildings in Costa Rica haven’t been well planified. They have been built following the natural shape of the terrain in a sort of least effort way, which is not flat at all, but has many hills, it goes up and down a lot. This reminds me a bit about geodesics, shortest curves in a geometric structure, but instead of minimizing distance we minimize effort or some sort of land transformation.