Braid group

Computational Aspects in the Braid Group and Applications to Cryptography - Mina Teicher

Mina Teicher Bar-Ilan University; Member, School of Mathematics March 12, 2012 The braid group on n strands may be viewed as an infinite analog of the symmetric group on n elements with additional topological phenomena. It appears in several areas of mathematics, physics and computer scien

From playlist Mathematics

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

Cyclic Groups (Abstract Algebra)

Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s

From playlist Abstract Algebra

Heinrich Matzat: Braids and Galois 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 SPECIAL 7th European congress of Mathematics Berlin 2016.

María Cumplido Cabello: Complexes of parabolic subgroups for Artin groups

Abstract : One of the main examples of Artin groups are braid groups. We can use powerful topological methods on braid groups that come from the action of braid on the curve complex of the n-puctured disk. However, these methods cannot be applied in general to Artin groups. In this talk we

From playlist Virtual Conference

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

Dihedral Group (Abstract Algebra)

The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo

From playlist Abstract Algebra

Braid group actions and PBW type basis pt2 - Calder Morton-Ferguson

Quantum Groups Seminar Topic: Braid group actions and PBW type basis pt2 Speaker: Calder Morton-Ferguson Affiliation: Massachusetts Institute of Technology Date: March 11, 2021 For more video please visit http://video.ias.edu

From playlist Quantum Groups Seminar

Introduction to Fiber Bundles part 2: Structure Groups

This is an important notion where we the transition functions of a certain fiber bundles lie in a smaller subgroup. This is important for setting up Streenrod's theorem.

From playlist Fiber bundles

Bert Wiest: Pseudo-Anosov braids are generic

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 Geometry

Dale Rolfsen: Braids, Orderings and Minimal Volume Cusped Hyperbolic 3-Manifolds

Dale Rolfsen, University of British Columbia Title: Braids, Orderings and Minimal Volume Cusped Hyperbolic 3-Manifolds The orderability properties of fundamental groups of minimal volume cusped hyperbolic 3-manifolds will be explored using the theory of braids and automorphisms of free gro

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Jack Morava: On the group completion of the Burau representation

Abstract: On fundamental groups, the discriminant ∏i≠k(zi – zk) ∈ C^× of a finite collection of points of the plane defines the abelianization homomorphism sending a braid to its number of overcrossings less undercrossings or writhe. In terms of diffeomorphisms of the punctured plane, it

From playlist SMRI Algebra and Geometry Online

Partitions of n-valued maps: a meal in four courses

A research talk presented at the Farifield University Mathematics Research Seminar, February 12, 2021. Should be accessible to a general mathematics audience. The paper: https://arxiv.org/abs/2101.09326

From playlist Research & conference talks

The affine Hecke category is a monoidal colimit - James Tao

Geometric and Modular Representation Theory Seminar Topic: The affine Hecke category is a monoidal colimit Speaker: James Tao Affiliation: Massachusetts Institute of Technology Date: February 24, 2021 For more video please visit http://video.ias.edu

From playlist Seminar on Geometric and Modular Representation Theory

Calista Bernard - Applications of twisted homology operations for E_n-algebras

An E_n-algebra is a space equipped with a multiplication that is commutative up to homotopy. Such spaces arise naturally in geometric topology, number theory, and mathematical physics; some examples include classifying spaces of braid groups, spaces of long knots, and classifying spaces of

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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

Kyle Hayden - A user's guide to building ribbon surfaces and holomorphic curves in 4-manifolds

June 21, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry We'll review a variety of hands-on ways to build ribbon surfaces in 4-manifolds, with an eye towards building holomorphic curves and symplectic/Lagrang

From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I

Eugene Gorsky - Algebra and Geometry of Link Homology 1/5

Khovanov and Rozansky defined a link homology theory which categorifies the HOMFLY-PT polynomial. This homology is relatively easy to define, but notoriously hard to compute. I will discuss recent breakthroughs in understanding and computing Khovanov-Rozansky homology, focusing on connecti

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

Alexei Davydov: Condensation of anyons in topological states of matter & structure theory

Condensation of anyons in topological states of matter and structure theory of E_2-algebras Abstract: The talk will be on the algebraic structure present in both parts of the title. This algebraic story is most pronounced for E2-algebras in the category of 2-vector spaces (also known as b

From playlist SMRI Seminars

Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra