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Korman Center, Room 245


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Faculty Candidate Seminar: Positivity, complexity, and the Kronecker problem abstract

Monday, February 4, 2013

3:00 PM-4:00 PM

Please join the Mathematics Department for a Faculty Candidate Seminar featuring Jonah Blasiak who is currently in the mathematics department at the University of Michigan.

Abstract: Positivity problems in algebraic combinatorics ask to find positive combinatorial formulae
for nonnegative quantities arising in geometry and representation theory like cohomological dimensions and dimensions of algebras and their irreducible representations.

A famous open positivity problem in representation theory is the Kronecker problem, which asks for a positive combinatorial formula for decomposing tensor products of irreducible representations of the symmetric group.

We will begin with a general discussion of positivity problems and an intriguing new motivation for these problems from complexity theory. We will then present our solution to a special case of the Kronecker problem that substantially improves on previous results.