Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Semi-coarse Spaces, Homotopy [Jonathan Treviño-Marroquín]
Semi-coarse spaces is an alternative to study (undirected) graphs through large-scale geometry. In this video, we present the structure and a homotopy what we worked on. In the final part, we look at the fundamental homotopy group of cyclic graphs.
From playlist Contributed Videos
What are differential equations?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Differential equations are usually classified into two general categories: partial differential equations, which are also called partial derivatives, and ordinary differential equations. Part
From playlist Popular Questions
Inner & Outer Semidirect Products Derivation - Group Theory
Semidirect products are a very important tool for studying groups because they allow us to break a group into smaller components using normal subgroups and complements! Here we describe a derivation for the idea of semidirect products and an explanation of how the map into the automorphism
From playlist Group Theory
Multivariable Calculus | Definition of partial derivatives.
We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties
Tudor Dimofte - 3d SUSY Gauge Theory and Quantum Groups at Roots of Unity
Topological twists of 3d N=4 gauge theories naturally give rise to non-semisimple 3d TQFT's. In mathematics, prototypical examples of the latter were constructed in the 90's (by Lyubashenko and others) from representation categories of small quantum groups at roots of unity; they were rece
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Inna Entova-Aizenbud: Jacobson-Morozov Lemma for Lie superalgebras using semisimplification
I will present a generalization of the Jacobson-Morozov Lemma for quasi-reductive algebraic supergroups (respectively, Lie superalgebras), based on the idea of semisimplification of tensor categories, which will be explained during the talk. This is a joint project with V. Serganova.
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Frobenius exact symmetric tensor categories - Pavel Etingof
Geometric and Modular Representation Theory Seminar Topic: Frobenius exact symmetric tensor categories Speaker: Pavel Etingof Affiliation: Massachusetts Institute of Technology Date: May 12, 2021 For more video please visit https://www.ias.edu/video
From playlist Seminar on Geometric and Modular Representation Theory
Thorsten Heidersdorf: On fusion rules for supergroups
I will report on some recent progress to understand the indecomposable summands in tensor products of irreducible representations of an algebraic supergroup. I will focus on the $GL(m|n)$ and $OSp(m|2n)$-case.
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Quiver moduli and applications, Markus Reineke (Bochum), Lecture 3
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 22
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
Flow on quiver representations, nested logarithms, and weight filtrations... - Fabian Haiden
Speaker:Fabian Haiden Topic: Flow on quiver representations, nested logarithms, and weight filtrations in artinian categories Affiliation: Harvard Date: November 11, 2016
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
Julia Plavnik: "Classifying small fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Classifying small fusion categories" Julia Plavnik - Indiana University, Mathematics Abstract: Classifying fusion categories is a problem that at the moment seems out of reach, since it includes the classification of finite groups and sem
From playlist Actions of Tensor Categories on C*-algebras 2021
GT23. Composition and Classification
Abstract Algebra: We use composition series as another technique for studying finite groups, which leads to the notion of solvable groups and puts the focus on simple groups. From there, we survey the classification of finite simple groups and the Monster group.
From playlist Abstract Algebra
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 14
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