My research interests are broadly related to algebraic geometry, algebraic topology, and number theory. In particular, I enjoy thinking about arithmetic-geometric questions through the lens of algebraic topology. My primary area of work is A1-enumerative geometry. This consists of using A1-homotopy theory to generalize classical enumerative theorems over algebraically closed fields into enumerative theorems over arbitrary perfect fields. I am also interested in classical algebraic geometry, anabelian geometry, and motivic homotopy theory.
My papers can be found here.
In layman's terms, I am interested in numbers and shapes. Numbers and shapes lie at the heart of mathematics. Number theory is the study of the patterns and structures of prime numbers, integers, rational numbers, and so on. The world of numbers is closely tied to algebra, and algebraic geometry provides a way of translating algebra into geometry. This translation lets us think about numbers by thinking about shapes like the one to the rightbelow. Algebraic topology is the study of shapes, including more complicated shapes like the one to the rightbelow. It provides several useful tools that help us think about them, which improves our understanding of algebra, so that we can finally gain insights about numbers.