Date and location: October 7, 2025, SC 1404
Speaker: Qirui Li (Pohang University of Science and Technology, Korea)
Title: Relative Trace Formulas, Arithmetic Fundamental Lemmas, and Derivatives of L-Functions
Abstract: The study of special values and derivatives of automorphic L-functions reveals deep connections between arithmetic geometry and harmonic analysis. A central theme is the Arithmetic Fundamental Lemma (AFL), which predicts precise identities between orbital integrals and intersection numbers of cycles. While methods based on perverse sheaves have achieved remarkable results in the function field case, they often obscure the underlying local geometry.
In this talk I will present recent progress on the higher linear AFL through the framework of the Relative Trace Formula (RTF). This approach provides explicit structural links between analytic orbital integrals and local intersection theory, enabling direct local proofs beyond global sheaf-theoretic methods. I will also outline several new directions: extending the AFL to the non-basic and conductor cases, and exploring their applications to global conjectures on derivatives of L-functions, including variants of Gross–Zagier type formulas.
Date and location: Sepember 23, 2025, SC 1404
Speaker: Brandon Alberts (Eastern Michigan University)
Title: Counting Number Fields via Multiple Dirichlet Series
Abstract: We describe a new technique for counting number fields using the theory of multivariable complex analytic functions. This method can be used to improve inductive counting methods for G-extensions when G is not “concentrated”, that is when we do not expect there to be an accumulating subfield. As an example, we prove the existence of an asymptotic growth rate for the number of G-extensions with bounded discriminant when G is a nilpotency class 2 group, subject to a certain analytic assumption that follows from the generalized Lindel\”of hypothesis. This is joint work with Alina Bucur.