Ralph Kaufmann: Graph Hopf algebras and their framework
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: I will discuss recent results linking the Hopf algebras of Goncharov for multiple zetas, the Hopf algebra of Connes and Kreimer for renormalis
From playlist Workshop: "Amplitudes and Periods"
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Number Theory | Hensel's Lemma
We prove Hensel's Lemma, which is related to finding solutions to polynomial congruences modulo powers of primes. http://www.michael-penn.net Thumbnail Image: By Unknown - Universität Marburg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9378696
From playlist Number Theory
Euclid rationalizing Lie groups: SO(2, ℚ) ⊂ U(1)
Lie Theory Reading Group: https://discord.gg/MNtv4mFTkJ In this video we're discussing Euclid's theorem about Pythagorean triples from a Lie group sort of angle. The text with all the links shown is found under https://gist.github.com/Nikolaj-K/015b23249d5aa92741f3e78f48fd6464 Two minor t
From playlist Algebra
Walter Van SUIJLEKOM - Renormalization Hopf Algebras and Gauge Theories
We give an overview of the Hopf algebraic approach to renormalization, with a focus on gauge theories. We illustrate this with Kreimer's gauge theory theorem from 2006 and sketch a proof. It relates Hopf ideals generated by Slavnov-Taylor identities to the Hochschild cocycles that are give
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
More arithmetic with polynumbers | Arithmetic and Geometry Math Foundations 59 | N J Wildberger
Polynumbers are extensions of numbers, but with a richer arithmetic. We will use them to provide a more solid foundation for the study of polynomials. Here we look at multiplying a positive polynumber by a scalar or number, connecting the multiplication of polynumbers with ordinary multip
From playlist Math Foundations
Linear Algebra 5.1 Eigenvalues and Eigenvectors
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Loïc FOISSY - Cointeracting Bialgebras
Pairs of cointeracting bialgebras recently appears in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, Manchon), graphs (Manchon), posets... We will give several results obtained on pairs of cointeracting bialgebras: act
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Advice | Exponentializing polyseries to get triangular on-maxels, and tilde Euler polynomials
Motivated by the relation between Bernoulli numbers and Bernoulli polynomials, we introduce a very general and powerful approach to move from sequences or polyseries to families of polynomials or polynumbers. When we apply this to the Euler numbers, we obtain a variant of the usual Euler
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer 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 Algebra
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
Guangyu Zhu: The Galois group of the category of mixed Hodge Tate structures
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: The category of mixed Hodge-Tate structures over Q is a mixed Tate category of homological dimension one. By Tannakian formalism, it is equiva
From playlist Workshop: "Periods and Regulators"
The Hopf Fibration via Higher Inductive Types - Peter Lumsdaine
Peter Lumsdaine Dalhousie University; Member, School of Mathematics February 13, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Introduction to quantized enveloping algebras - Leonardo Maltoni
Quantum Groups Seminar Topic: Introduction to quantized enveloping algebras Speaker: Leonardo Maltoni Affiliation: Sorbonne University Date: January 21, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Chapter 7 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Homological algebra 1: Tor for abelian groups
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give two examples to motivate the definition of the groups Tor(A,B), from the universal coefficient theorem of algebraic t
From playlist Commutative algebra
On the classification of fusion categories – Sonia Natale – ICM2018
Algebra Invited Lecture 2.5 On the classification of fusion categories Sonia Natale Abstract: We report, from an algebraic point of view, on some methods and results on the classification problem of fusion categories over an algebraically closed field of characteristic zero. © Interna
From playlist Algebra