Everyone is welcome to attend the presentation. *Refreshments will be served in the lounge at 1:30 p.m.!*

Wednesday, April 6, 2022 at 2:00 p.m.

PhD Candidate: Malors Espinosa Lara

Supervisor: Jim Arthur

Thesis title: Explorations on Beyond Endoscopy

***

In this thesis we provide a description of the first paper on Beyond Endoscopy by Altu˘g and explain how to generalize to totally real fields, based on a joint work of the author with Melissa Emory, Debanjana Kundu and Tian An Wong, and is a work in preparation. This part is mostly expository, and we refer the reader to the relevant paper [7] Furthermore, we prove a conjecture of Arthur. In his original paper on Beyond

Endoscopy, Langlands provides a formula for certain product of orbital integrals in GL(2, Q), subsequently used by Altu˘g to manipulate the regular elliptic part of the trace formula with the goal of isolating the contribution of the trivial representation. Arthur predicts this formula should coincide with a product of polynomials associated to zeta functions of orders constructed by Zhiwei Yun. We prove this is the case by finding the explicit polynomials and recovering the original formula from them.

We also explain how some aspects of the strategy used can be interpreted as problems of independent interest and importance of their own.

***

A draft of the thesis is available here: Malors_Espinosa_PhD_Thesis_8FEB2022

## no comment as of now