The Shapiro-Shapiro Conjecture
Iain Gordon (University of Edinburgh)
Monday 21st April, 2008 16:00-17:00 214, Mathematics Building
The Shapiro-Shapiro conjecture (from the early 90s) is a simple statement on a relationship between a family complex polynomials and their Wronskian. The conjecture has nice consequences which include the reality of Schubert calculus on Grassmannians. In full generality, the conjecture was proved in 2005 by Mukhin, Tarasov and Varchenko using the Bethe Ansatz for the Gaudin Model. I will present a new proof of this result which uses work of Wilson on Calogero-Moser spaces and adelic Grassmannians to translate the conjecture to a purely representation theoretic question on symplectic reflection algebras which turns out to be elementary to confirm. This is joint with Milen Yakimov and Emil Horozov.