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
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
Algebraic topology: Fundamental group of a knot
This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx
From playlist Algebraic topology
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
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
Cyclic Groups, Generators, and Cyclic Subgroups | Abstract Algebra
We introduce cyclic groups, generators of cyclic groups, and cyclic subgroups. We discuss an isomorphism from finite cyclic groups to the integers mod n, as well as an isomorphism from infinite cyclic groups to the integers. We establish a cyclic group of order n is isomorphic to Zn, and a
From playlist Abstract Algebra
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
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
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
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
Ö. Yurttas - Algorithms for multicurves with Dynnikov coordinates
Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system. In this talk we describe polynomial time algorithms for cal
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
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
David BROADHURST - Tasmanian Adventures
I report on two adventures with Dirk Kreimer in Tasmania, 25 years ago. One of these, concerning knots, is not even wrong. The other, concerning a conjectural 4-term relation, is either wrong or right. I suggest that younger colleagues have powerful tools that might be brought to bear on t
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
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
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
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.
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
Topologically Ordered Matter and Why You Should be Interested by Steven H. Simon
COLLOQUIUM TOPOLOGICALLY ORDERED MATTER AND WHY YOU SHOULD BE INTERESTED SPEAKER: Steven H. Simon (Oxford University, United Kingdom) DATE: Mon, 26 October 2020, 15:30 to 17:00 VENUE: Online ABSTRACT In two dimensional topologically ordered matter, processes depend on gross topology
From playlist ICTS Colloquia
Visual Group Theory, Lecture 2.1: Cyclic and abelian groups
Visual Group Theory, Lecture 2.1: Cyclic and abelian groups In this lecture, we introduce two important families of groups: (1) "cyclic groups", which are those that can be generated by a single element, and (2) "abelian groups", which are those for which multiplication commutes. Addition
From playlist Visual Group Theory