The Number Theory group at the CRM investigates deep arithmetic phenomena through the lens of the Langlands Program, which connects number theory, representation theory, and algebraic geometry. Our research seeks to understand the arithmetic of Galois representations, automorphic forms and abelian varieties.
Part of our work concerns the use of modularity lifting theorems and the modular method to address Diophantine problems, such as those arising in the study of rational points on curves. We also apply p-adic methods to the Birch and Swinnerton-Dyer conjecture, and to the construction and computation of special cycles, points, and cohomology classes on Shimura varieties.
Our work is both theoretical and computational, and we aim to develop new frameworks and techniques that not only advance fundamental understanding, but also inform broader developments in arithmetic geometry.
The group’s activity is highly collaborative, with strong ties to international research networks in number theory and related fields.
GROUP LEADERS
