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
Dimitry Gurevich - From Reflection Equation Algebra to Matrix Models
Reflection Equation Algebra is one of the Quantum matrix algebras, associated with a given Hecke symmetry, i.e. a braiding of Hecke type. I plan to explain how to introduce analogs of Hermitian Matrix Models arising from these algebras. Some other applications of the Reflection Equation Al
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
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
An Introduction To Group Theory
I hope you enjoyed this brief introduction to group theory and abstract algebra. If you'd like to learn more about undergraduate maths and physics make sure to subscribe!
From playlist All Videos
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Lattices, Hecke Operators, and the Well-Rounded Retract - Mark McConnell
Mark McConnell Center for Communications Research, Princeton University March 7, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Hecke Endomorphism Algebras, Stratification, finite groups of Lie type, and ı-quantum algebras
Recorded for UVa Conference Presented by Jie Du (joint work with B. Marshall and L. Scott)
From playlist Pure seminars
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
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
Modular forms and multiple q-Zeta values (Lecture 2) by Ulf Kuehn
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
Matt Hogancamp: Soergel bimodules and the Carlsson-Mellit algebra
The dg cocenter of the category of Soergel bimodules in type A, morally speaking, can be thought of as a categorical analogue of the ring of symmetric functions, as in joint work of myself, Eugene Gorsky, and Paul Wedrich. Meanwhile, the ring of symmetric functions is the recipient of acti
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
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
Pseudorepresentations and the Eisenstein ideal - Preston Wake
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Pseudorepresentations and the Eisenstein ideal Speaker: Preston Wake Affiliation: University of California, Los Angeles Date: November 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
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
Ring Definition (expanded) - Abstract Algebra
A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin
From playlist Abstract Algebra
New developments in the theory of modular forms... - 9 November 2018
http://crm.sns.it/event/416/ New developments in the theory of modular forms over function fields The theory of modular forms goes back to the 19th century, and has since become one of the cornerstones of modern number theory. Historically, modular forms were first defined and studied ov
From playlist Centro di Ricerca Matematica Ennio De Giorgi