(Conjectural) triply graded link homology groups of the Hopf link and Hilbert schemes of points on the plane

Friday, February 29, 2008 -
2:00pm to 4:00pm
Gukov et al. suggested triply graded link homology groups via refined BPS counting on the deformed conifold. Through large N duality they identify their PoincarĂ© polynomials as refined topological vertices. I further apply the geometric engineering to interpret them as holomorphic Euler characteristics of natural vector bundles over Hilbert schemes of points on the affine plane. Then they perfectly make sense mathematically. This work is very preliminary, but I hope it could be developed further.
Speaker: 
Hiraku Nakajima
Kyoto University and IAS
Event Location: 
Fine Hall 314