This seminar series usually meets on Wednesday afternoon 3:30pm - 5pm online.


Sep. 21 Stefan SchreiederZoom link Password: 976309
Oct. 5Olivier BenoistZoom: 915 8535 2473Password: abc123
Nov. 9 Mingmin Shen Tencent Meeting Password: see talk information
Nov. 23 Lie Fu Zoom link Password: see talk information
Nov. 30 Zsolt Patakfalvi Zoom link meeting id: 645 7050 0045
Dec. 14 Jean Fasel Zoom link

Talk information

Jean Fasel (Grenoble)

Time: Dec. 14, 15:30-17:00

Zoom link ID : 933 2147 8124 Code secret : 895850

Title: Vector bundles on threefold

Abstract: In this talk, I will survey classification results for vector bundles on threefolds. I will start with classical results in the affine case, and then show how to complete the classification in that case. Then, I will pass to quasi-projective threefolds, focusing on the case of complex varieties.

Zsolt Patakfalvi (Lausanne)

Time November 30, 15:30-17:00

Zoom link meeting id: 645 7050 0045

Title: Local Kawamata-Viehweg vanishing for excellent 3-folds

Abstract: I will present a joint work with Emelie Arvidsson and Fabio Bernasconi about proving the local Kawamata-Viehweg vanishing in general for excellent 3-folds, excluding residue characteristics 2,3 and 5. This is a vanishing of local cohomology at those points of log-canonical pairs that are not log-canonical centers. The consequence is that if we apply Minimal Model Program to find 1-parameter stable degenerations of surfaces, then the obtained limit is S_2 and hence it is indeed a stable limit in the sense of Kollar and Shepherd-Barron. In particular, the properness of the moduli space of stable surfaces over Z1/30 reduces to proving the open question called locally stable reduction.

Lie Fu (Strasbourg)

Time: November 23, 16:00-17:00 (Note the unusual starting time !)

Zoom Link Meeting ID: 545 921 0876 Meeting password: 540902

Title: Some finiteness results for projective hyper-Kaehler varieties.

Abstract: I will report on a recent joint work with Zhiyuan Li, Teppei Takamatsu, and Haitao Zou, on the unpolarized Shafarevich conjecture for hyper-Kaehler varieties: it is about the finiteness (up to isomorphism) of such varieties defined over a number field with good reductions outside a fixed finite set of place. In the proof, we will make use of some uniform version of the Kuga-Satake construction, inspired by Yiwei She's work in the case of K3 surfaces.

Mingmin Shen (Amsterdam)

Time: November 9, 15:30-17:00

TencentMeetingļ¼š974-9834-0582 Meeting Link Meeting Password: 2022??, ??=number of lines in a smooth cubic surface.

Title: The Grothendieck period conjecture on a product of elliptic curves

Abstract: The Hodge conjecture predicts that a class in the Betti cohomology of a smooth projective variety is the class of an algebraic cycle if it is a Hodge class. In the algebraic de Rham cohomology, one can also ask which classes are actually algebraic. A conjectural answer to this question is the Grothendieck period conjecture (GPC). In this talk, I will outline a proof of the GPC on an abelian variety isogeneous to a product of elliptic curves. This is joint work with Charles Vial.

Olivier Benoist (Paris)

Time: October 5, 15:30-17:00

Zoom ID: 915 8535 2473 Password: abc123

Title: Algebraic cohomology classes and smooth subvarieties.

Abstract: Can all algebraic cohomology classes on a smooth projective complex variety be written as linear combinations of classes of smooth subvarieties? The answer to this question is negative, by work of Hartshorne, Rees and Thomas. In this talk, we will review what is known about this problem, and we will describe new counterexamples. This is partly joint work with Olivier Debarre.

Stefan Schreieder (Hannover)

Time: September 21, 15:30-17:00

Zoom Link Password: 976309

Title: A moving lemma for cohomology with support.

Abstract: For a natural class of cohomology theories with support, we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit a smooth projective compactification. This has the following consequences for such k-varieties and cohomology theories: a local and global generalization of the effacement theorem of Quillen, Bloch–Ogus, and Gabber, a finite level version of the Gersten conjecture in characteristic zero, and a generalization of the injectivity property and the codimension 1 purity theorem for 'etale cohomology. Our results imply that refined unramified cohomology groups of smooth projective varieties are motivic invariants.