2008-2009

Mike O'Neill

**Monday, October 6
**Sprague Library, 3rd
floor seminar space (Harvey Mudd)

**Title: **The Riesz
rearrangement inequality and a problem in additive number theory

Abstract: Riesz’s rearrangement inequality involves a convolution of three functions f, g, and h and states that such a convolution is dominated by the same convolution of the radially symmetric decreasing rearrangements f*, g* and h* of the original f, g and h. A characterization of the cases of equality in Riezs’s inequality was obtained a few years ago by Burchard. In joint work with undergraduates, I helped to determine the cases of equality in an inequality of Pollard from additive number theory. In this talk, I will survey the above two problems and show how they are connected.