Department of Mathematics - Master Calendar

Analysis seminar

Speaker: Bruce Reznick (UIUC)

Title: Deeper arithmetic-geometric inequalities

Abstract: 

The arithmetic-geometric inequality can be derived by forcing a second-order zero at (1,1,...,1) on a sum of monomials, whose exponents consist of a simplex with one interior point. What happens when you force a fourth-order zero at (1,1,...,1)? There will be some partial results. This talk needs a large number of elementary techniques which will be fully explained, including Newton polytopes, Laguerre's extension of Descartes' Rule of Signs, Vandermonde determinants, exponential polynomials, and the Rabinowitsch trick. I tried to give talks on this forty years ago and nobody could figure out what I was talking about. I'm determined not to repeat that outcome this time.