Mark W. McConnell: Computing Hecke operators for cohomology of arithmetic subgroups of SL_n(Z)
Abstract: We will describe two projects. The first which is joint with Avner Ash and Paul Gunnells, concerns arithmetic subgroups Γ of G=SL_4(Z). We compute the cohomology of Γ∖G/K, focusing on the cuspidal degree H^5. We compute a range of Hecke operators on this cohomology. We fi Galois
From playlist Number Theory
A Satake Isomorphism Mod.p - Guy Henniart
A Satake Isomorphism Mod.p Guy Henniart November 4, 2010 Let F be a locally compact non-Archimedean field, p its residue characteristic and G a connected reductive algebraic group over F . The classical Satake isomorphism describes the Hecke algebra (over the field of complex numbers) of
From playlist Mathematics
Abstract Algebra | The notion of a subgroup.
We present the definition of a subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
Xuhua He: Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras
SMRI Algebra and Geometry Online: Xuhua He (Chinese University of Hong Kong) Abstract: Let G(ℂ) be a complex reductive group and W be its Weyl group. In 1966, Tits introduced a certain subgroup of G(ℂ), which is an extension of W by an elementary abelian 2-group. This group is called the
From playlist SMRI Algebra and Geometry Online
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Algorithms for the topology of arithmetic groups and Hecke actions - Michael Lipnowski
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Algorithms for the topology of arithmetic groups and Hecke actions Speaker: Michael Lipnowski Affiliation: Member, School of Mathematics Date: November 6, 2017 For more videos, please visit htt
From playlist Mathematics
Nigel Higson: Isomorphism conjectures for non discrete groups
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I shall discuss aspects of the C*-algebraic version of the Farrell-Jones conjecture (namely the Baum-Connes conjecture) for Lie groups and p-adic groups. The conj
From playlist HIM Lectures: Junior Trimester Program "Topology"
Shimura Varieties and the Bernstein Center - Tom Haines
Shimura Varieties and the Bernstein Center - Tom Haines University of Maryland; von Neumann Fellow, School of Mathematics December 6, 2010 The local Langlands conjecture (LLC) seeks to parametrize irreducible smooth representations of a p-adic group G in terms of Weil-Deligne parameters. B
From playlist Mathematics
Corina Ciobotaru: Analytic aspects of locally compact groups
The theory of unitary representations describes locally compact groups from the point of view of harmonic analysis and operator theory. To provide a good understanding there are various concepts that are considered. In this talk I present recent results and open questions regarding the Hec
From playlist HIM Lectures: Junior Trimester Program "Topology"
Ana Caraiani - 2/3 Shimura Varieties and Modularity
We describe the Calegari-Geraghty method for proving modularity lifting theorems beyond the classical setting of the Taylor-Wiles method. We discuss the three conjectures that this method relies on (existence of Galois representations, local-global compatibility and vanishing of cohomology
From playlist 2022 Summer School on the Langlands program
Ben Elias: Categorifying Hecke algebras at prime roots of unity
Thirty years ago, Soergel changed the paradigm with his algebraic construction of the Hecke category. This is a categorification of the Hecke algebra at a generic parameter, where the parameter is categorified by a grading shift. One key open problem in categorification is to categorify He
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Local-global compatibility in the crystalline case - Ana Caraiani
Joint IAS/Princeton University Number Theory Seminar Topic: Local-global compatibility in the crystalline case Speaker: Ana Caraiani Affiliation: Imperial College Date: April 16, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Dennis Gaitsgory. A toy model for the Drinfeld-Lafforgue shtuka construction
Abstract: The goal of this talk is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of departure the Hecke action of Rep(G^L) on the category Shv(Bun_G) of sheaves on Bun_G, and also
From playlist CORONA GS
Ana Caraiani - 3/3 Shimura Varieties and Modularity
We discuss vanishing theorems for the cohomology of Shimura varieties with torsion coefficients, under a genericity condition at an auxiliary prime. We describe two complementary approaches to these results, due to Caraiani-Scholze and Koshikawa, both of which rely on the geometry of the H
From playlist 2022 Summer School on the Langlands program
Clément Dell’aiera - Paires de Hecke et K-théorie
Introduites par Shimura en théorie des nombres dans les années 50, les paires de Hecke sont des inclusions de sous-groupes qui sont presque normales : leurs conjugués sont tous commensurables. À une paire de Hecke est associée un groupe localement compact totalement discontinu : sa complét
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Panorama of Mathematics: Peter Scholze
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Peter Scholze: "Locally sym
From playlist Panorama of Mathematics
Sophie Morel - 1/3 Shimura Varieties
Depending on your point of view, Shimura varieties are a special kind of locally symmetric spaces, a generalization of moduli spaces of abelian schemes with extra structures, or the imperfect characteristic 0 version of moduli spaces of shtuka. They play an important role in the Langlands
From playlist 2022 Summer School on the Langlands program
Stephane Gaussent, Research talk - 3 February 2015
Stephane Gaussent (Université Jean Monnet - Saint Etienne) - Research talk http://www.crm.sns.it/course/4445/ Spherical, Hecke or Iwahori-Hecke algebras associated to a reductive group over a local field are well known and have a lot of applications in representation theory. Braverman, Ka
From playlist Lie Theory and Representation Theory - 2015