Presented by: 
Paul Zinn-Justin (Universite Pierre et Marie Curie, Jussieu)
Date: 
Mon 24 Mar, 2:00 pm - 2:45 pm
Venue: 
Hawken Engineering Building (50), room N202

In this work in collaboration with A. Knutson, we investigate the correspondence between algebraic geometry and quantum integrable systems from the point of view of Grobner degenerations. The latter is very combinatorial in nature and at a technical level, applies equally well to cohomology and K-theory. Following Knutson and Miller, I shall describe the simplest framework in which this approach works, namely (matrix) Schubert varieties and Schubert polynomials. I shall next formulate several variations and extensions, which will lead us naturally to loop models on 2d lattices and to the Yang--Baxter equation: first noncrossing loops (Temperley--Lieb model), then crossing loops (Brauer model).