Where: Zoom

Speaker: Federico Scavia (UBC) - http://www.math.ubc.ca/~scavia/

Abstract: Let k be a field. Totaro studied the de Rham cohomology of algebraic stacks

over k, and computed it for classifying stacks of linear algebraic k-groups

in many cases. Combining previous work of Drury, May and Epstein, I define

and study Steenrod operations on the de Rham cohomology of smooth algebraic

stacks over a field k of characteristic p>0. These operations share many

properties with their topological analogues, but there are also important

differences. I then determine the Steenrod operations on the de Rham

cohomology of linear algebraic k-groups computed by Totaro.

Where: Zoom

Speaker: Wenhao Ou (Chinese Academy of Sciences) - https://sites.google.com/site/wenhaooumath/

Abstract: After a theorem of Andreatta and Wisniewski, if the tangent bundle of a projective manifold X contains an ample subsheaf, then X is isomorphic to projective space. We show that, if the tangent bundle contains a strictly nef subsheaf, then X is a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group of X is virtually abelian, then X is isomorphic to a projective space. This is joint with Jie Liu and Xiaokui Yang.

Where: Online

Speaker: Krishna Hanumanthu ( Chennai Mathematical Institute) - https://www.cmi.ac.in/~krishna/

Abstract: Seshadri constants of nef line bundles on projective varieties were defined by Demailly in 1990, motivated by an ampleness criterion of Seshadri. They are a measure of local positivity of line bundles, have interesting connections to the geometry of the variety, and their study is now an active area of research. We will give an overview of the current work in this area and discuss some recent results on Grassmann bundles over curves and Bott towers.

Where: Zoom

Speaker: Si Ying Lee (Harvard) - https://www.math.harvard.edu/people/leesi-ying/

Abstract: The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschebung. Blasius and Rogawski proposed a generalization of this result for general Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about recent work on this conjecture for Shimura varieties of Hodge type.

Where: https://umd.zoom.us/j/96890967721

Speaker: Sam Mundy (Columbia University) -

Abstract: In this talk I'll give an overview of the method of Skinner--Urban method for constructing Selmer classes for certain Galois representations which have an automorphic origin. I'll explain some recent progress in trying to apply this method for the exceptional group G_2 to obtain Selmer classes for the symmetric cube of certain GL_2 Galois representations.

Where: Zoom

Speaker: Arthur-Cesar Le Bras (Institut Galilee, Universite Paris 13) - http://lebras.perso.math.cnrs.fr/

Abstract: In 2014, Fargues formulated a striking conjecture, which veryroughly says that geometric Langlands works over the Fargues-Fontaine

curve and provides a geometrization of the classical local Langlands

correspondence. In my first talk, I will recall what the main geometric

players are, and what the conjecture says, with special emphasis on the

case of GL_n. In my second talk, I would like to discuss work in

progress with Johannes Anschutz, regarding the case where the group is

GL_n and where one starts with an irreducible (instead of any

indecomposable) Weil-Deligne representation in the conjecture.

Where: via Zoom, link on seminar page

Speaker: Maria Yakerson (ETH Zurich) -

https://www.muramatik.com/

Abstract: Various invariants have been computed for Hilbert schemes of surfaces, however our knowledge about Hilbert schemes (of points) of higher dimensional schemes is quite limited. For example, Hilbert schemes of n-dimensional affine spaces have very complicated geometry for high n. In this talk we will present the surprising observation, that the Hilbert scheme of infinite dimensional affine space has homotopy type of a Grassmannian, and so its invariants of homotopical nature have a simple description. We will explain then how this observation allows us to obtain new properties of algebraic and hermitian K-theories as generalized cohomology theories. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.

Where: Zoom

Speaker: Arthur-Cesar Le Bras (Institut Galilee, Universite Paris 13) - http://lebras.perso.math.cnrs.fr/

Abstract: In 2014, Fargues formulated a striking conjecture, which veryroughly says that geometric Langlands works over the Fargues-Fontaine

curve and provides a geometrization of the classical local Langlands

correspondence. In my first talk, I will recall what the main geometric

players are, and what the conjecture says, with special emphasis on the

case of GL_n. In my second talk, I would like to discuss work in

progress with Johannes Anschutz, regarding the case where the group is

GL_n and where one starts with an irreducible (instead of any

indecomposable) Weil-Deligne representation in the conjecture.

Where: Zoom

Speaker: Nikita Semenov (LMU (Munich)) - http://www.mathematik.uni-muenchen.de/~semenov/

Abstract: Let G be a split semisimple algebraic group over a field and

let A be an oriented cohomology theory in the sense of Levine--Morel. We

provide a uniform approach to the A-motives of geometrically cellular

smooth projective G-varieties based on the Hopf algebra structure of

A(G). Using this approach we provide various applications to the

structure of motives of twisted flag varieties. This is a joint work

with Victor Petrov.

Where: Zoom

Speaker: Nicola Tarasca (Virginia Commonwealth University) - http://people.vcu.edu/~tarascan/

Abstract: This talk will focus on geometric realizations of non-commutative algebras. I will discuss how representations of conformal vertex algebras encode information about the geometry of algebraic curves. The starting point is the Virasoro uniformization, which provides an incarnation of the Virasoro algebra in the tangent space of a tautological line bundle on the moduli space of coordinatized curves. After briefly reviewing vertex algebras, I will discuss how their representations yield new vector bundles of conformal blocks on moduli spaces of curves and new cohomological field theories. This is joint work with Chiara Damiolini and Angela Gibney.

Where: Zoom

Speaker: Wei Zhang (MIT) - http://math.mit.edu/~wz2113/

Abstract: The arithmetic fundamental lemma (AFL) is an identity relating the arithmetic intersection numbers on a Rapoport-Zink space for unitary groups to the first derivative of relative orbital integral on the general linear groups over a p-adic field F. In this talk I will report a work in progress joint with A. Mihatsch to prove the AFL for a general p-adic field. We also establish a partial analog (over totally real fields) of a theorem of Bruinier--Howard--Kudla--Rapoport--Yang on the modularity of generating series of arithmetic special divisors.

Where: Online

Speaker: Niranjan Ramachandran (UMD) - https://www-math.umd.edu/people/faculty/item/442-atma.html

Abstract: A recent conjecture of S. Lichtenbaum provides Euler characteristic-type formulas for the special values of zeta functions of proper regular schemes over Z.

The talk will discuss the case of the special value at s=1 of an arithmetic surface; we shall indicate the relations with the BSD conjecture and the Bloch-Kato conjecture. This is joint work with Lichtenbaum.

Where: Online

Speaker: Shizhang Li (University of Michigan, Ann Arbor) - http://shizhang.li/

Abstract: In this talk I will explain an upcoming joint work with Tong Liu establishing a comparison between prismatic and certain A_{crys}-type crystalline cohomology. I shall first introduce some reasons why one expects such a comparison. Then I'll explain the statement of this comparison and give some applications (specialize in the Breuil--Kisin prism setup).

Where: Online

Speaker: Priyankur Chaudhuri (University of Maryland) -

Abstract: TBA

Where: Online

Speaker: Lukas Brantner (Oxford University) -

Where: Online

Speaker: Oishee Banerjee (HCM Bonn) - https://www.math.uni-bonn.de/people/oishee/

Abstract: TBA

Where: Online

Speaker: Kai-Wen Lan (U. Minnesota) -