Calendar

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Olivia Beckwith, Tulane University
Polyharmonic Maass forms and Hecke series for real quadratic fields

We study polyharmonic Maass forms and show that they are related to ray class extensions of real quadratic fields. In particular, we generalize work of Lagarias and Rhoades to give a basis for the space of polyharmonic Maass forms for $\Gamma(N)$. Modifying an argument of Hecke, we show that twisted traces of cycle integrals of certain depth 2 polyharmonic Maass forms are leading coefficients of Hecke $L$-series of real quadratic fields. This is ongoing joint work with Gene Kopp.

Event contact: Gene Kopp

Posted January 16, 2026

Algebra and Number Theory Seminar Questions or comments?

Koustav Mondal, Louisiana State University
TBA

Event contact: Gene Kopp

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Marco Sangiovanni Vincentelli, Columbia University
An Euler system for the adjoint of a modular form

Euler systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of $L$-functions. However, despite the key role they have played in making progress toward foundational conjectures in number theory, such as the Birch and Swinnerton-Dyer and Bloch–Kato Conjectures, only a handful of provably non-trivial Euler systems have been constructed to date. A significant obstacle to constructing Euler Systems lies in producing candidate Galois cohomology classes. This lecture series presents joint work with Chris Skinner that develops a method to overcome this obstacle. Using this method, we construct an Euler system for the adjoint of a modular form.

Event contact: Gene Kopp

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Kiran Kedlaya, University of California San Diego
TBA

Event contact: Gene Kopp