# Colloquium abstracts

**Kartik Prasanna**

University of Michigan, USA

August 27, 2015

**Arithmetic and geometric aspects of the Jacquet-Langlands correspondence**: The Jacquet-Langlands correspondence is one of the simplest examples of Langlands functoriality. While it has been known for several decades (being the culmination of the famous book by Jacquet and Langlands on automorphic forms) and has played a key role in number theory (for example in the proof of Fermat via Ribet's theorem on level-lowering), many arithmetic and geometric aspects of this correspondence remain quite mysterious. I will give an overview of some of these questions and what is known about them, explaining the relation to problems in the theory of algebraic cycles.