University of Chicago Algebraic Geometry Seminar
The algebraic geometry seminar is held in Eckhart Hall room 203,
on Wednesdays at 4-5pm, unless otherwise specified.
here to see the location of Eckhart Hall, and
here for driving directions to University of Chicago.
Click here to see older talks.
Fall 2010 Seminars
Christian Schnell (University of Illinois at Chicago):
Derived Equivalence and the Picard Variety
Abstract: I will explain a result, joint with Mihnea Popa, saying that
if two smooth projective varieties have equivalent derived categories of
coherent sheaves, then their Picard varieties are isogeneous. In
particular the number of independent holomorphic one-forms is a derived
invariant. A consequence of this is that derived equivalent threefolds
have the same Hodge numbers.
October 15 (Friday, 2.30pm, note special date and time)
Sabin Cautis (Columbia University): Categorified Heisenberg actions on
Abstract: I will describe an action of a quantized Heisenberg algebra on the (derived) categories of coherent sheaves on Hilbert schemes of ALE spaces (crepant resolutions of C^2/G). This action essentially lifts the actions of Nakajima and Grojnowski on the cohomology of these spaces. (joint with Tony Licata)
Timothy Logvinenko: Spherically orthogonal objects and spherical fibrations
Abstract: Seidel and Thomas introduced some years ago a notion of a spherical
object in the derived category D(X) of a smooth projective variety X.
We introduce a relative analogue of this notion by defining what does
it mean for an object E of the derived category D(Y x X) of a fiber
product of two schemes X and Y to be spherical over Y.
A categorical equivalent of a subscheme of X fibered over Y is an
object of D(Y x X) orthogonal over Y. We show that such objects are
spherical over Y if and only if they possess certain simple cohomological
properties similar to those in the original definition of a spherical
object. We then interpret this geometrically in the special case where
our objects are actual flat fibrations in X over Y.
This is a joint work with Rina Anno of UChicago.
Jean Fasel: Grothendieck-Witt groups and projective modules
Abstract: We will present new developments in the theory of
Grothendieck-Witt groups (aka Hermitian K-theory), and then give some nice
applications. In particular, we will sketch a proof of Suslin's conjecture that stably
free modules of rank d-1 over a smooth affine algebra of dimension d
over an algebraically closed field are free.
Damien Megy: Examples of variation of Hodge structure over projective varieties
Abstract: I will talk about a family of examples of variations of Hodge structure over some smooth projective varieties and give an outline of the construction of these varieties. Then, I will explain how to use Morihiko Saito's decomposition theorem to compute certain cohomological invariants of these objects.
Here is a link to the complete seminar list
If you have a request for a future speaker or any questions, please
contact Luca Scala (email@example.com).