Lathisms
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José was born and raised in Escuinapa, a small city in the southern border of the Mexican state of
Sinaloa. He moved to Mexico City to do his undergrad studies in Mathematics at Universidad Nacional
Autónoma de México (UNAM). After a master's degree at Ohio University, he completed his PhD at
Northeastern University in Boston, Massachusetts, under the supervision of Ivan Losev. He had
postdoctoral positions at the University of California, Davis and at the Max-Planck Institute for
Mathematics in Bonn, Germany. In the fall of 2022, he came back to Mexico for a tenure track position at
UNAM's Instituto de Matemáticas, where he has been since.
José works at the interface between representation theory, algebraic geometry and combinatorics. He is
interested in using combinatorial techniques in order to better understand structures appearing in algebra
and algebraic geometry. This can be, for example, through the construction of explicit bases of
representations of an algebra and a combinatorial analysis of the action in these bases. The
representations are oftentimes realized as an invariant (such as (co)homology or K-theory) of an
algebraic variety, so the combinatorics are intimately related to the geometry of the corresponding variety.
José is also interested in the theory of cluster algebras, a family of commutative algebras admitting a
distinguished family of recursively constructed generators, and which often underlie positivity phenomena.
With his collaborators, he imported techniques from contact and symplectic geometry in order to give a
cluster algebra structure to the coordinate algebra of a wide family of algebraic varieties. The construction
of these cluster algebra structures unifies and generalizes many of the foundational examples of cluster
algebras and opens a new window in the study of important varieties that appear naturally in the study of
representations of Lie algebras.
“Besides celebrating the culture and talent found in Latin American communities, Hispanic Heritage
Month is also an opportunity to create a thriving community. I would not be where I am today without the
help and support of an enormous number of mentors, friends, collaborators, and allies. I consider it my
responsibility to uplift the younger generations of Latinx Mathematicians, so that our voices continue to
resonate even stronger within the wider mathematical community.”