On the modularity of genus 2 curves

We will give an accessible introduction to the Hasse-Weil conjecture for curves and related problems in the Langlands program. We will discuss some recent work with G. Boxer, F. Calegari and T. Gee in which we prove the modularity of a positive proportion of genus two curves. We will explain some analogies with geometric representation theory which inspired certain parts of our work.

Vincent Pilloni is the Director of Mathematics Research at CNRS. You can learn more about Vincent Pilloni on his website.