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
Modular forms: Hecke operators
This lecture is part of an online graduate course on modular forms. We introduce Hecke operators for modular functions in three different ways. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj51HisRtNyzHX-Xyg6I3Wl2F
From playlist Modular forms
In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.
From playlist Abstract algebra
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
Abstract Algebra | The third isomorphism theorem for groups.
We prove the third isomorphism theorem for groups. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
A derived Hecke algebra in the context of the mod pp Langlands program -Rachel Ollivier
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: A derived Hecke algebra in the context of the mod pp Langlands program Speaker: Rachel Ollivier Affiliation: University of British Columbia Date: November 8, 2017 For more videos, please visit
From playlist Mathematics
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
Geometric Categorifications of the Hecke Algebra - Laura Rider
2021 Women and Mathematics Colloquium Topic: Geometric Categorifications of the Hecke Algebra Speaker: Laura Rider Affiliation: University of Georgia Date: May 26, 2021 In the first part of this talk, I'll explain a geometric categorification of the Hecke algebra in terms of perverse sh
From playlist Mathematics
Michael Harris: Construction of p-adic L-functions for unitary groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 4
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
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
Quantum Groups Seminar Topi: R-matrices II Elijah Bodish University of Oregon Date: February 25, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Periods, cycles, and L-functions: A relative trace formula approach – Wei Zhang – ICM2018
Number Theory Invited Lecture 3.10 Periods, cycles, and L-functions: A relative trace formula approach Wei Zhang Abstract: Motivated by the formulas of Gross–Zagier and Waldspurger, we review conjectures and theorems on automorphic period integrals, special cycles on Shimura varieties, a
From playlist Number Theory
Ting Xue: Character sheaves, Hecke algebras and Hessenberg varieties
28 September 2021 Abstract: We discuss character sheaves in the setting of graded Lie algebras. Via a nearby cycle construction irreducible representations of Hecke algebras of complex re ection groups at roots of unity enter the description of character sheaves. Recent work of Lusztig an
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Intermediate Algebra-Inverse Functions
Intermediate Algebra-Inverse Functions
From playlist Intermediate Algebra
Fred Diamond, Geometric Serre weight conjectures and theta operators
VaNTAGe Seminar, April 26, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Ash-Sinott: https://arxiv.org/abs/math/9906216 Ash-Doud-Pollack: https://arxiv.org/abs/math/0102233 Buzzard-Diamond-Jarvis: https://www.ma.imperial.ac.uk/~buzzard/maths/research/paper
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
The K-ring of Steinberg varieties - Pablo Boixeda Alvarez
Geometric and Modular Representation Theory Seminar Topic: The K-ring of Steinberg varieties Speaker: Pablo Boixeda Alvarez Affiliation: Member, School of Mathematics Date: February 03, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
The picture in the lecture was taken from Wikipedia: https://en.wikipedia.org/wiki/Demographics_of_the_United_States#/media/File:USA2020dec1.png
From playlist Abstract Algebra 1