Algebraic Geometry Seminar Fall 2011

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The seminar meets on Fridays at 2:25 pm in Van Vleck B215.

The schedule for the previous semester is here.

Fall 2011

date speaker title host(s)
Sep. 23 Yifeng Liu (Columbia) Enhanced Grothendieck's operations and base change theorem for

sheaves on Artin stacks

Tonghai Yang
Oct. 7 Zhiwei Yun (MIT) Cohomology of Hilbert schemes of singular curves Shamgar Gurevich
Oct. 14 Javier Fernández de Bobadilla (Instituto de Ciencias Matematicas, Madrid) Nash problem for surfaces
Nov. 25 Shamgar Gurevich (Madison) Canonical Hilbert Space: Why? How? and its Categorification


Title: Enhanced Grothendieck's operations and base change theorem for sheaves on Artin stacks

Abstract: Laszlo and Olsson have conditionally defined Grothendieck's six operations for sheaves on Artin stacks, and proved the base change theorem on the cohomological level. I will explain a new approach toward the theory of sheaves on Artin stacks in very general set-ups. With this approach, the base change theorem follows in a natural way. Our method relies on the theory of infinity categories developed by Lurie. This is a joint work with Weizhe Zheng.

Spring 2012

date speaker title host(s)
May 4 Mark Andrea de Cataldo (Stony Brook) TBA Maxim

Abstracts

Yifeng Liu

TBA


Zhiwei Yun

Cohomology of Hilbert schemes of singular curves

Abstract: For a smooth curve, the Hilbert schemes are just symmetric powers of the curve, and their cohomology is easily computed by the H^1 of the curve. This is known as Macdonald's formula. In joint work with Davesh Maulik, we generalize this formula to curves with planar singularities (which was conjectured by L.Migliorini). In the singular case, the compactified Jacobian will play an important role in the formula, and we make use of Ngo's technique in his celebrated proof of the fundamental lemma.