| Speaker: | Abhiram M. Kidambi (MPI-MiS) |
|---|---|
| Title: | Modularity theorems beyond elliptic curves |
| Date (JST): | Tue, Sep 09, 2025, 13:30 - 15:00 |
| Place: | Seminar Room A |
| Abstract: |
The modularity theorems are powerful statements in arithmetic geometry and link number theory, harmonic analysis and geometry and form a key part of the Langlands program. The most famous example of a modularity theorem is the proof of the Taniyama-Shimura-Weil conjecture by Wiles; Wiles-Taylor; Breuil-Conrad-Diamond-Taylor which states that every elliptic curve over Q has an associated weight 2 cusp form on some arithmetic congruence subgroup of SL(2,Z) which captures information of number of solutions to the elliptic curve equation over finite fields. Modularity conjectures have been generalized to other curves, surfaces and varieties in general such as abelian varieties, K3 surfaces and even rigid Calabi-Yau 3-folds. In this talk, I will give an overview of modularity theorems for some of the known cases. I will discuss modularity of certain non-rigid CY manifolds. There are applications of modularity theorems in mathematical physics and Diophantine analysis and I will not discuss this in the talk so I welcome interactions during my 4 week stay here at IPMU. |
