The Waring problem and group theory
The Waring problem and group theory

Michael Larsen , Indiana University
Fine Hall 314
The Waring problem asks whether for each positive integer n, every positive integer is the sum of a bounded number of nth powers. Although Hilbert solved it more than 100 years ago, it remains the focus of much current research. I will discuss some questions in group theory, especially algebraic group theory, inspired by it. In particular, I will present work with Aner Shalev and Pham Tiep on Waringtype word maps on finite simple groups and work with Dong Quan Ngoc Nguyen on the unipotent Waring problem. The emphasis throughout will be on unsolved problems.