Optimization, Complexity and Invariant Theory

Abstract: Many important problems in computational complexity can be rewritten in the language of invariant theory. Famous examples include the graph isomorphism problem, and the GCT approach to P vs NP. The focus of this talk will be to illustrate the rich interaction between algebra and algorithms in invariant theory. We will work closely with the examples of matrix invariants and semi-invariants where the algebraic and algorithmic aspects aid each other's progress.