Algebra Seminar

No occurrence obstructions in geometric complexity theory

Peter Burgisser (Technical University of Berlin)

Wednesday, October 10, 2018 11:15 am
MONT 313 (Storrs)

The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP and VNP. Mulmuley and Sohoni suggested to study a strengthened version of this conjecture over the complex numbers that amounts to separating the orbit closures of the determinant and padded permanent polynomials. In that paper it was also proposed to separate these orbit closures by exhibiting occurrence obstructions, which are irreducible representations of GL_{n^2}(C), which occur in one coordinate ring of the orbit closure, but not in the other. Recently it was shown by us that this approach is impossible. On the positive side, this research has led to new and surprising insights about Kronecker coefficients and plethysm coefficients.