Uploaded May 2026 | Updated September 2026, 3 weeks ago
Joint IAS/PU Number Theory
3:30pm|Simonyi 101 and Remote Access
Topic: On the Distribution of Modular Points on Deformation Rings
Speaker: John Bergdall
Affiliation: University of Arkansas
Date: April 30, 2026
The goal of this talk is to discuss a new local-global phenomenon in the Langlands program on automorphic forms and Galois representations. Spaces of modular forms are parametrized by weights, and those same weights parametrize local deformation rings defined by conditions in p-adic Hodge theory. In the mid-2000's, M. Kisin's work on modularity showed that modular points can be found on each and every component of one of these local deformation rings. The purpose of this talk is to describe an extension of Kisin's result, by giving a specific method for counting how many points a given component has in terms of that component's special fiber geometry. This is joint work with Chengyang Bao (Imperial College, London) and Brandon Levin (Rice University, Houston).
Joint IAS/PU Number Theory
3:30pm|Simonyi 101 and Remote Access
Topic: On the Distribution of Modular Points on Deformation Rings
Speaker: John Bergdall
Affiliation: University of Arkansas
Date: April 30, 2026
The goal of this talk is to discuss a new local-global phenomenon in the Langlands program on automorphic forms and Galois representations. Spaces of modular forms are parametrized by weights, and those same weights parametrize local deformation rings defined by conditions in p-adic Hodge theory. In the mid-2000's, M. Kisin's work on modularity showed that modular points can be found on each and every component of one of these local deformation rings. The purpose of this talk is to describe an extension of Kisin's result, by giving a specific method for counting how many points a given component has in terms of that component's special fiber geometry. This is joint work with Chengyang Bao (Imperial College, London) and Brandon Levin (Rice University, Houston).
