Computational Complexity in Algebraic Combinatorics

Representation theoretic multiplicities are at the heart of many open
problems in algebraic combinatorics. At the same time these
quantities appear in Geometric Complexity Theory in the search for
multiplicity obstructions for separating computational complexity
classes like VP vs VNP. Most recently they have also been considered
in quantum computing.
In this talk we will introduce the objects and problems, explain how
formalization through computational complexity theory could answer
some of the open problems in the negative. We will also explain their
role in GCT and quantum computing with a mixture of positive and
negative answers.