Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing

Yuanzhi Li

This workshop aims to explore connections between complexity and optimization with algebra and analysis, which have emerged from the works on operator scaling. The hope is to inform participants from different communities of both basic tools and new developments, and set out new challenges and directions for this exciting interdisciplinary research. Some of the topics and notions that will be explored include:Optimization: Alternate minimization. Scaling algorithms. Gradient methods for geodesic convexity. Brascamp-Lieb polytopes. Entropy optimality.Invariant Theory: Linear group actions, and degree bounds on invariant rings. Nullcone and orbit closure intersection problems. Moment polytopes. Non-commutative duality. Algorithms avoiding Grobner bases.Computational complexity: Commutative and non-commutative arithmetic circuits. Symbolic matrices. Polynomial identity testing. Tensor rank. Geometric complexity theory.Quantum Information Theory: Completely positive operators. Quantum distillation. Entanglement polytopes. https://www.ias.edu/math/ocit2018/agenda

https://www.ias.edu/video/OCIT/2018/0607-YuanzhiLi