I was born in 1994, Concepción, Chile.
Concepción, Chile.
I did my bachelor in Mathematics at Universidad de Concepción, between 2012 and 2013, during this period I studied Algebraic Geometry under the advice of Antonio Laface. My first encounter with Algebraic Geometry was focused on linear systems of hypersurfaces and problems around the SHGH conjecture.
In 2014, I started my master in Mathematics at Universidad de Concepción, and I devoted some time to do research in the topology and singularities of algebraic varieties with torus action. During this period my advisor was Antonio Laface and my co-advisor Alvaro Liendo.
Universidad de Concepción, Chile.
In Fall 2015, I started my Ph.D in Mathematics at University of Utah, USA. During my Ph.D I worked on questions around the minimal model program under the advice of Christopher Hacon. I finished my Ph.D in the summer of 2019. My thesis contained some new results regarding termination of flips.
University of Utah, USA.
In Fall 2019, I started working at Princeton University as an Instructor in Mathematics. During my stay at Princeton, together with several co-authors, we proved new results regarding log terminal singularities: their topology, reductive quotients, and minimal log discrepancies. We also gave a characterization of toric singularities from the perspective of the singularities of the minimal model program.
Princeton University, USA.
In Fall 2022, I started working at UCLA as a tenure-track Assistant Professor.
During this time, I am mostly performing research on structural theorems for Fano varieties and Calabi-Yau varieties.
A motivating question is whether we can describe a large class of Fano varieties using combinatorial language. Toric Fano varieties already form a quite interesting class of Fano varieties that are purely combinatorial in nature. However I expect that this class should be enlarged in such a way that it contains more birational modifications of toric varieties. For this reason I introduced two invariants: the coregularity and the birational complexity. Recently, I've been studying how these two invariants reflect in the geometry of Fano and Calabi-Yau varieties. The results on this direction are expected to apply to the study of klt singularities.
UCLA, Los Angeles, USA.