Avi Wigderson: Operator scaling - theory and applications

In this talk I will explain the ``singularity problem'' for symbolic matrices over non commuting variables, and describe its myriad origins and incarnations in commutative and non-commutative algebra, computational complexity, optimization, quantum information theory, Brascamp-Lieb inequalities and other areas. I will describe the ``Operator scaling'' algorithm, which efficiently solves all these related problems, and how its analysis combines ideas from these areas. This algorithm efficiently solves a large family of non-convex optimization problems, and will hopefully find other applications.

I will elaborate on algebraic and analytic aspects of this work (respectively) in the two following lectures on May 23 and May 24. Based on joint works with Ankit Garg, Leonid Gurvits and Rafael Olivera.