EPSILON DICHOTOMY FOR LINEAR MODELS (Analytic, geometric and $p$-adic aspects of automorphic forms and $L$-functions)

Abstract

This is an expanded version of my talk at the RIMS conference "Analytic, geometric and p-adic aspects of automorphic forms and L-functions". It surveys some recent work towards a conjecture of Prasad and Takloo-Bighash on epsilon dichotomy for linear models. I thank the organizers of the conference for their hospitality. I am also grateful to Miyu Suzuki for her help during the preparation of this note. This work is partially supported by the NSF grant DMS #1901862.