Mathematics Department Colloquium: Operator scaling - theory and applications

Colloquium | February 16 | 4:10-5 p.m. | 60 Evans Hall

 Avi Wigderson, IAS

 Department of Mathematics

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. The algorithm efficiently solves a non-convex optimization problem, and will hopefully have many other applications.