About Bhargav Bhatt's Work
My research interests lie at the intersection of two fields of mathematics: algebraic geometry (which studies solutions to systems of polynomial equations in many variables) and number theory (which studies properties and relationship of numbers). The interaction between these fields, which dates back thousands of years, is often mediated through a third field: topology (which studies the qualitative features of shapes). My research exploits this connection to transport problems in one field to potentially more tractable problems in the other.
For example, in the past, I have used number-theoretic ideas to solve problems in algebraic geometry. In the next few years, I propose working on a program that would use insights from topology to elucidate the behavior of certain subtle and poorly understood objects in number theory; the path to this goal passes through various facets of algebraic geometry, and thus has purely geometric consequences as well.