Quantitative Uniform Convexity Bounds and their Application

Thursday, February 19, 2015 - 2:00pm - 3:00pm
Lind 305
Eric Carlen (Rutgers, The State University Of New Jersey )
Quantitative uniform convexity bounds for the unit ball in a Banach space have many applications. The sharp 2-uniform convexity bounds for the Schatten trace norms (tracial analogs of the L^p norms) we proven by Ball, Lieb and myself, and were applied by Lieb and myself to prove a conjecture of Gross on hypercontractivity. The sharp form of this inequality has found many applications since then, including in my own more recent work. Certain of these applications, along with open problems, will be discussed.