Alexei Oblomkov
<br>
Title: Cohomology ring of the compactified Jacobian of the
plane curve
$x^m=y^n$
<br>
Abstract: Joint work with Zhiwei Yun.
In elementary terms the compactified Jacobian   $JC_{m,n}$ 
is the moduli space of subspaces $L\subset \CC[[t]]$  of
codimension $(m-1)(n-1)$ that are preserved by multiplication
on $t^m$ and $t^n$. Together with Zhiwei Yun we described an
action of the spherical rational Cherednik
algebra $eH_{m/n}(S_n)e$ on $H^*(JC_{m,n})$ and  the ring
structure of the
cohomology. I will also discuss perverse filtration on
cohomology  $H^*(JC_{m,n})$ and connections  with $q,t$-Catalan
numbers.