The algebraic geometry seminar is held in Eckhart Hall room 203, on Wednesdays at 4-5pm, unless otherwise specified.

Click here to see the location of Eckhart Hall, and here for driving directions to University of Chicago.

Click here to see older talks.

October 6

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 Hilbert schemes

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)

October 20

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.

October 27

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.

November 10

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 (lucascala@math.uchicago.edu).