#### Thursday March 22, 2018 1:00 p.m. Yost, 306

**Title: **Convex Analysis and its application to Quantum Information Theory

**Student:** Ben Li

**Advisors:** Dr. Elisabeth Werner and Dr. Stanislaw Szarek

**Abstract: **My PhD thesis addresses problems on mathematical aspects of Quantum information theory and convex geometry. This expository talk will consist of two parts. In the first part, we will discuss the non-locality problem of the quantum world, which usually attracts most attention in this context, from the mathematical point of view it is equally striking that – at least for bipartite systems and dichotomic measurements – the discrepancy between classical and quantum correlations cannot be arbitrarily large: it can not exceed the so-called Grothendieck constant. This is a consequence of the seminal work of Tsirelson and the even more famous Grothendieck inequality from functional analysis. We calculate analytically the exact values of quantum violations for the Bell correlation inequalities that appear in the setups involving up to four measurements; they are all smaller than √ 2.