Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
Rings and modules 2: Group rings
This lecture is part of an online course on rings and modules. We decribe some examples of rings constructed from groups and monoids, such as group rings and rings of Dirichlet polynomials. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrm
From playlist Rings and modules
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
0:00 Motivation for studying modules 4:45 Definition of a vector space over a field 9:31 Definition of a module over a ring 12:12 Motivating example: structure of abelian groups 16:05 Motivating example: Jordan normal form 19:44 What unifies both examples (spoiler): Structure theorem for f
From playlist Abstract Algebra 2
Programming Ruby 03 -- Basic Types
An overview of the basic types in Ruby -- strings, integers, arrays, and hashes.
From playlist Programming: Ruby
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
This lecture is part of an online course on rings and modules. We mainly discuss the problem of whether free modules over a ring have a well defined ran, generalizing the dimension of a vector space. We show that they do over many rings, including all non-zero commutative rings, but give
From playlist Rings and modules
Paul-André Melliès - A Functorial Excursion between Algebraic Geometry and Linear Logic
In this talk, I will use the functor of points approach to Algebraic Geometry to establish that every covariant presheaf X on the category of commutative rings — and in particular every scheme X — comes equipped “above it” with a symmetric monoidal closed category PshModX of presheaves of
From playlist Combinatorics and Arithmetic for Physics: special days
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
Representations on KU-modules - David Treumann
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Representations on KU-modules Speaker: David Treumann Affiliation: Boston College Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Vanessa Miemietz: A categorified double centraliser theorem and applications to Soergel bimodules
I will explain how notions from classical representation theory, including a double centraliser theorem, lift to finitary 2-representation theory, and how this helps in classifying simple 2-representations of Soergel bimodules of finite Coxeter type in characteristic zero.
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Catherine Meusburger: Turaev-Viro State sum models with defects
Talk by Catherine Meusburger in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 17, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Generic bases for cluster algebras (Lecture 2) by Pierre-Guy Plamondon
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
A Hecke action on the principal block of a semisimple algebraic group - Simon Riche
Workshop on Representation Theory and Geometry Topic: A Hecke action on the principal block of a semisimple algebraic group Speaker: Simon Riche Affiliation: Université Paris 6; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 16
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
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
Sam Gunningham: Character stacks and (q−)geometric representation theory
Abstract: I will discuss applications of geometric representation theory to topological and quantum invariants of character stacks. In particular, I will explain how generalized Springer correspondence for class D-modules and Koszul duality for Hecke categories encode surprising structure
From playlist Algebraic and Complex Geometry