Kloosterman sums, Maass forms, and partitions.

This talk is about three important objects in number theory and the relationships between them.

The partition function counts the number of ways to break a natural number into parts—it is a fundamental object in combinatorics and additive number theory.

Kloosterman sums are exponential sums which appear naturally in a wide range of applications in number theory.

Maass forms are certain automorphic forms which encode information about a variety of arithmetical problems.

I will describe the objects and their history, the connections between them, some deep conjectures about their properties, and some recent results.

This will be a non-technical talk and will hopefully be accessible (and interesting!) to a general mathematical audience

Scott Ahlgren is a Professor of Mathematics at the University of Illinois.

He earned a Ph.D. in 1996 under the supervision of Wolfgang Schmidt

at the University of Colorado and held positions at Penn State University

and Colgate University before joining the faculty at Illinois in 2001.

He has authored more than 50 papers on various topics in number theory.

This is his third visit to BYU.