Hopf algebra

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

What is the Hopf Fibration?

In this video I shed some light on a heavily alluded to and poorly explained object, the Hopf Fibration. The Hopf Fibration commonly shows up in discussions surrounding gauge theories and fundamental physics, though its construction is not so mysterious.

From playlist Summer of Math Exposition Youtube Videos

Hopf Fibration 1

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/1mUo

From playlist 3D printing

Hopf link bagel

A bagel cut into a Hopf link.

From playlist Algebraic Topology

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

Giovanni Landi: The Weil algebra of a Hopf algebra

We generalize the notion, due to H. Cartan, of an operation of a Lie algebra in a graded differential algebra. Firstly, for such an operation we give a natural extension to the universal enveloping algebra of the Lie algebra and analyze all of its properties. Building on this we define the

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

Hopf Fibration (grid)

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3bz5

From playlist 3D printing

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

Algebra - Ch. 4: Exponents & Scientific Notation (1 of 35) What is an Exponent?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an exponent. A number or symbol placed above another number or symbol that indicates the power the number or symbol at the bottom is raised. The number at the bottom is called the base

From playlist ALGEBRA CH 4 EXPONENTS AND SCIENTIFIC NOTATION

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

Dimensions Chapter 7

Chapter 7 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

Symmetric Groups (Abstract Algebra)

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in

From playlist Abstract 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