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#Algebraic Structures

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NPTEL

Linear Algebra

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The main purpose of this course is the study of linear operators on finite dimensional vector spaces. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications.
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60 Lesons
1 day 9 hours
On-Demand
Free-Video
NPTEL

Commutative Algebra

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Comprehensive exploration of commutative algebra concepts through 60 lectures, covering fundamental principles and advanced topics for a deep understanding of algebraic structures.
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61 Lesons
1 day 5 hours
On-Demand
Free-Video
GOTO Conferences

Computation as Semigroups, Computing Semigroups

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Explore the intersection of semigroups, computation, and functional programming. Gain insights into mathematical foundations of software engineering from a unique perspective.
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1 Lesons
26 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Algebraic Structure of Area-Preserving Homeomorphism Groups - Lecture 4

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Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Delve into link spectral invariants and Lagrangian Floer homology.
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1 Lesons
58 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 2

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Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Discover link spectral invariants and their role in solving this problem.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 1

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Explore the algebraic structure of area-preserving homeomorphism groups, focusing on Fathi's question and the simplicity conjecture for compact surfaces. Gain insights into link spectral invariants and their role in solving this problem.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Dr. Gajendra Purohit

Group Theory

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Comprehensive exploration of group theory, covering key concepts from basic definitions to advanced topics like Sylow theorems, ideal for mathematics and engineering students.
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62 Lesons
20 hours
On-Demand
Free-Video
Institute for Advanced Study

Introduction to Quantized Enveloping Algebras - Leonardo Maltoni

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Explore quantized enveloping algebras, their structure, and applications in quantum groups. Learn about Gaussian binomial coefficients, q-deformations, and Hopf algebra structures.
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15 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

An Introduction to Geometry and Dynamics on Semisimple Lie Groups - Part 1

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Explore semisimple Lie groups, their structure, discrete subgroups, and asymptotic behavior in this comprehensive introduction to geometry and dynamics.
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10 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Substitutions in Non-Commutative Multivariate Power Series

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Explore group laws on non-commutative formal power series, their structures, and applications in non-commutative probability theory through a Hopf algebraic approach.
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1 Lesons
46 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Hidden Symmetries in Fluid Dynamics - Lecture 8

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Explore hidden symmetries in fluid dynamics, focusing on theoretical foundations and applications to hydrodynamic turbulence. Gain insights into Kolmogorov self-similarity and intermittency through rigorous models and numerical challenges.
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1 Lesons
3 hours 26 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Hidden Symmetries in Fluid Dynamics - Lecture 7

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Explore hidden symmetries in fluid dynamics, focusing on theoretical foundations and applications to hydrodynamic turbulence. Gain insights into Kolmogorov self-similarity and intermittency through rigorous models and numerical challenges.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Hidden Symmetries in Fluid Dynamics - Lecture 5

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Explore hidden symmetries in fluid dynamics, focusing on theoretical foundations and applications to hydrodynamic turbulence. Gain insights into Kolmogorov self-similarity and intermittency through rigorous models and numerical challenges.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Hidden Symmetries in Fluid Dynamics - Lecture 4

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Explore hidden symmetries in fluid dynamics, focusing on theoretical foundations and applications to hydrodynamic turbulence. Gain insights into Kolmogorov self-similarity and intermittency through rigorous models and numerical challenges.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Equações de Grau Cinco

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Explore a complexidade das equações de grau cinco e suas soluções, aprofundando-se em conceitos matemáticos avançados e suas implicações teóricas.
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1 Lesons
40 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Categorification at Roots of Unity

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Explorez la catégorification des groupes quantiques aux racines de l'unité, en examinant les algèbres p-DG et les représentations catégoriques pour sl(2).
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1 Lesons
42 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spaces of Orderings and Applications - Lecture 4

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Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spaces of Orderings and Applications - Lecture 3

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Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
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1 Lesons
46 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spaces of Orderings and Applications - Lecture 1

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Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

R-matrices for the Category O of Quantum Loop Algebras

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Explore R-matrices for quantum loop algebras' category O, examining a functor relating Uq(g) and Uh(g) categories, and analyzing resulting R-matrices' properties and factorization.
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1 Lesons
35 minutes
On-Demand
Free-Video
CIMPA UCR

Contando Cuerpos de Números Algebraicos

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Explora la teoría de cuerpos de números algebraicos y sus aplicaciones en matemáticas avanzadas. Profundiza en conceptos fundamentales y técnicas de conteo.
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1 Lesons
59 minutes
On-Demand
Free-Video
CIMPA UCR

Una Introducción a las Álgebras de Vértices y sus Representaciones

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Explora las álgebras de vértices y sus representaciones, adentrándote en conceptos fundamentales y aplicaciones avanzadas en matemáticas teóricas.
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1 Lesons
47 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Differential Categories

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Explorez les catégories différentielles et leur application en logique linéaire différentielle dans cette conférence mathématique approfondie.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 18

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Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática e suas aplicações.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 17

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Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 26

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Explore advanced concepts in Lie Algebras, focusing on doctoral-level topics and theoretical foundations in this comprehensive lecture by Jethro Van Ekeren.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 25

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Explore conceitos avançados de Álgebras de Lie em uma aula de doutorado ministrada por Jethro Van Ekeren, aprofundando o conhecimento em matemática pura.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 22

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Explore advanced concepts in Lie Algebras, focusing on doctoral-level topics and theoretical foundations in this comprehensive lecture by Jethro Van Ekeren.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 20

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Explore conceitos avançados de Álgebras de Lie em uma aula de doutorado ministrada por Jethro Van Ekeren, aprofundando o conhecimento em matemática pura.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 19

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Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Models of Consciousness Conferences

Sketches of a Mathematical Theory of Qualia

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Exploración matemática de los qualia: definición, estructura y relación con la teoría cuántica. Propone un modelo de conciencia basado en principios abstractos del comportamiento de dispositivos que detectan qualia.
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22 Lesons
20 minutes
On-Demand
Free-Video
Simons Institute

Algebraic Structures in Logic and Query Evaluation - Part 2

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Explore advanced algebraic structures in logic and their applications to database query evaluation, building on fundamental concepts.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Simons Institute

Algebraic Structures in Logic and Query Evaluation - Part 1

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Explore algebraic structures' role in logic and query evaluation, focusing on their applications in database theory and AI algorithms.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Simons Institute

Algebraic Structures in Logic and Query Evaluation - Lecture 3

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Explore algebraic structures in logic and query evaluation, focusing on advanced concepts and their applications in database theory and AI.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Institute

Algebraic Structures in Logic and Query Evaluation - Part 4

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Explore algebraic structures' role in logic and query evaluation, focusing on advanced concepts and their applications in database theory and AI.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Insights into Mathematics

Geometric Graph Theory - Weyl Groups, Root Systems and Quadratic Forms

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Explore geometric graph theory through the Mutation Game, examining root systems, Weyl groups, and quadratic forms. Discover how graphs generate unique geometrical structures and reflection groups.
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11 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

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Explore complex numbers and their connection to plane rotations, laying the groundwork for understanding quaternions and 3D rotations. Emphasizes a logical, algebraic approach without relying on transcendental functions.
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11 Lesons
58 minutes
On-Demand
Free-Video
Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

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Explore quaternions and their connection to 3D rotations using 2x2 complex matrices. Learn key formulas and visual models for this algebraic structure without relying on transcendental concepts.
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9 Lesons
56 minutes
On-Demand
Free-Video
Michael Penn

The Universal Enveloping Algebra

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Explore the concept of universal enveloping algebra, its construction, properties, and applications in abstract algebra and representation theory.
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1 Lesons
29 minutes
On-Demand
Free-Video
Michael Penn

A Commutative Vertex Algebra

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Explore the universal commutative vertex algebra with one generator, demonstrating how to give a polynomial ring vertex algebra structure through an in-depth mathematical analysis.
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1 Lesons
35 minutes
On-Demand
Free-Video
Michael Penn

The Normally Ordered Product

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Explore the concept of normally ordered product in vertex algebras, its definition, and importance in understanding vertex operator structures.
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1 Lesons
32 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - Ideals of Quotients of PIDs

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Explore the proof that ideals in quotients of principal ideal domains are principal, delving into the intricacies of abstract algebra and ring theory.
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1 Lesons
24 minutes
On-Demand
Free-Video
Michael Penn

Abstract Algebra - A PID That Is Not a Euclidean Domain

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Explore a principal ideal domain that's not Euclidean, using Dedekind-Hasse Norm and universal side divisor concepts to demonstrate this intriguing algebraic property.
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1 Lesons
37 minutes
On-Demand
Free-Video
Michael Penn

Vertex Algebras - The Non-Negative Products

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Explore the structure of non-negative products in vertex algebras, delving into advanced mathematical concepts and their applications in algebraic theory.
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1 Lesons
24 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Sums in Progressions to Squarefree Moduli Among Polynomials Over a Finite Field

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Explore polynomial sums in progressions to squarefree moduli over finite fields, covering Fourier analysis, polynomial anatomy, and arithmetic functions.
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12 Lesons
58 minutes
On-Demand
Free-Video
International Mathematical Union

Stuart White- Classification of Simple Amenable C-Algebras

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Explore the classification of simple amenable C*-algebras with Stuart White, covering operator algebras, group actions, inductive limits, and the Elliott programme in this mathematical lecture.
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14 Lesons
47 minutes
On-Demand
Free-Video
International Mathematical Union

Hodge Theory, Between Algebraicity and Transcendence

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Explore recent advances in Hodge theory, comparing algebraic structures and bounding transcendence using o-minimal geometry. Gain insights into complex algebraic varieties and their applications.
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13 Lesons
42 minutes
On-Demand
Free-Video
International Mathematical Union

Character Estimates for Finite Simple Groups and Applications

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Explore character estimates for finite simple groups and their applications in various mathematical problems, including mixing times, Waring's Problem, and conjectures by Ore and Thompson.
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18 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Cyclotomic KLR Algebras - Part 1 of 4

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Exploring cyclotomic KLR algebras, their connection to quantum groups, and their role in categorifying highest weight representations, with a focus on type A and the Ariki–Brundan–Kleshchev theorem.
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13 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

Singular Chains on Lie Groups and the Cartan Relations

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Explore the connection between Lie group representations and infinitesimal descriptions using Cartan relations, with applications to Chern-Weil theory and higher local systems on classifying spaces.
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19 Lesons
51 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Skein Categories

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Explore skein categories, their relation to factorisation homology, and connections to stated skein algebras and Alekseev's moduli algebras in this advanced mathematical talk.
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12 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Iva Halacheva - The Cactus Group, Crystals, and Perverse Equivalences

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Exploring connections between cactus groups, crystals, and perverse equivalences in categorical actions of semisimple Lie algebras, focusing on Rickard complexes and their implications for derived categories.
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10 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

On Conjugacy of Cartan Subalgebras in Extended Affine Lie Algebras and Classification of Torsors

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Explore advanced concepts in extended affine Lie algebras and torsors over Laurent polynomial rings in this mathematical lecture by Vladimir Chernousov at the Fields Institute.
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15 Lesons
56 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Classifying Small Fusion Categories

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Explore the classification of small fusion categories, including recent results on odd-dimensional modular and fusion categories. Learn about different interpretations of "small" in this context.
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1 Lesons
33 minutes
On-Demand
Free-Video
IMSA

Braids and Line Arrangements - Old and New

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Explore the interplay between braid groups, configuration spaces, and hyperplane arrangements, focusing on recent advances in understanding fundamental groups of complex line arrangement complements.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Polynomials for Quivers and Topological Recursion

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Explore A-polynomials for quivers and their connection to topological recursion in this advanced mathematics lecture by Piotr Sułkowski from the University of Warsaw.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Algebraic Definition of Braids and the Braid Group

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Explore the algebraic foundations of braids and the braid group, delving into their mathematical properties and applications in topology and geometry.
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1 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Chiral Algebras from Three Dimensions

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Explore the fascinating connection between chiral algebras and three-dimensional physics in this advanced mathematical lecture by renowned physicist Sergei Gukov.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
ICTP Mathematics

A Geometric R-Matrix for the Hilbert Scheme of Points on a General Surface

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Explore geometric R-matrices for Hilbert schemes of points on general surfaces, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
ICTP Mathematics

Singularities via BCM Algebras

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Explore singularities through BCM algebras, delving into advanced mathematical concepts with expert insights from K. Tucker of the University of Illinois at Chicago.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Fields Institute

Arithmetic Occult Periods

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Explore surprising uniformizations of complex configuration spaces as arithmetic ball quotients, examining period maps and their algebraic structures in Shimura varieties.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Fields Institute

Euler Classes, Pairings, and Duality

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Explore Euler classes in modules, their connection to Hochschild homology pairings, and implications for various forms of duality in homotopy theory and arithmetic geometry.
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1 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Generalized Kac-Moody Superalgebras and Root Groupoid

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Explore advanced algebraic structures with Vera Serganova as she delves into Generalized Kac-Moody Superalgebras and Root Groupoid, offering insights for mathematicians and theoretical physicists.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Fields Institute

Strong Minimality and Algebraic Relations Between Solutions for Poizat's Family of Equations

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Explore strong minimality and algebraic relations in solutions for Poizat's equations, delving into advanced concepts in model theory and mathematical logic.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

F-rational Rings and Rational Singularities - Part 2

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Explore F-rational rings and rational singularities in depth, building on previous concepts and advancing understanding of tight closure theory in algebraic geometry.
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1 Lesons
55 minutes
On-Demand
Free-Video
ICTP Mathematics

F-rational Rings and Rational Singularities - Part 3

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Explore F-rational rings and rational singularities in this advanced mathematics lecture, delving into tight closure theory and its applications in algebraic geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Growth in Linear Algebraic Groups and Permutation Groups

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Exploración de límites de diámetro en grupos simétricos y algebraicos lineales, con énfasis en técnicas simplificadas y conexiones entre diferentes enfoques matemáticos.
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1 Lesons
45 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Thierry Coquand- Constructive Algebra

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Explore constructive algebra with Thierry Coquand, delving into foundational concepts and innovative approaches within the Types, Sets and Constructions program.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
QuantumTopology

Jacobians of Circulant Graphs

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Explore Jacobians of circulant graphs with A. D. Mednykh, delving into advanced mathematical concepts and their applications in graph theory and topology.
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1 Lesons
42 minutes
On-Demand
Free-Video
QuantumTopology

On Fundamental Properties of Skein Algebras of Surfaces

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Explore fundamental properties of skein algebras of surfaces with Adam Sikora in this insightful one-hour lecture on quantum topology.
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1 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Roe-Type Algebras and Their Isomorphisms

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Explore Roe-type algebras and their isomorphisms in this advanced mathematics talk by Alessandro Vignati, delving into operator algebras and their connections with logic.
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1 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Representations of P-Adic Groups and Hecke Algebras

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Explore p-adic group representations and Hecke algebras, focusing on supercuspidal representations, Bernstein blocks, and their equivalence to depth-zero blocks through Hecke algebra isomorphisms.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Topological Components of Commuting Elements of Nilpotent Lie Groups

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Explore topological components of commuting elements in nilpotent Lie groups, focusing on reduced upper unitriangular matrix groups and generalized Heisenberg groups. Discover connections to cohomology classes and symplectic Stiefel manifolds.
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1 Lesons
51 minutes
On-Demand
Free-Video
IMSA

Sophie Kriz, University of Michigan - Some Computations on FI-Modules

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Explores recent results on FI-modules in positive and mixed characteristic, including local cohomology computations and examples of simple generic FI-modules in positive characteristic.
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1 Lesons
55 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

A 2020 View of Fermat's Last Theorem

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Explore the historical journey and modern perspectives on Fermat's Last Theorem with renowned mathematician Kenneth A. Ribet in this insightful lecture from the 2020 Joint Mathematics Meetings.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Amenable Actions on Finite Simple C*-Algebras Arising From Flows on Pimsner Algebras

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Explore amenable actions on finite simple C*-algebras derived from flows on Pimsner algebras in this advanced mathematical talk by Yuhei Suzuki from Hokkaido University.
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1 Lesons
47 minutes
On-Demand
Free-Video
Simons Institute

Semiring-Based Soft Constraint Solving and Argumentation

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Explore semiring applications in constraint solving and argumentation, focusing on optimizing solutions beyond traditional problem-solving approaches.
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1 Lesons
29 minutes
On-Demand
Free-Video
Simons Institute

A -Semi-Ring-Based Query Algebra for Incremental View Maintenance and Query Compilation

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Algebraic approach to incremental view maintenance using ring structures. Introduces a powerful query calculus with polynomial normal form, enabling efficient delta queries and multi-layered maintenance schemes.
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1 Lesons
33 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Derived Microlocal Geometry and Virtual Invariants

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Explore derived microlocal geometry and its application to virtual invariants, including a 3D refinement of the 2D cohomological Hall algebra in this advanced mathematics lecture.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Insights into Mathematics

Platonic Solids and Their Symmetries - Dynamics on Graphs 10

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Explore Platonic solids' symmetries, focusing on rotations and reflections. Discover connections to exceptional structures in mathematics and physics, laying groundwork for understanding 4D regular solids.
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7 Lesons
26 minutes
On-Demand
Free-Video
Insights into Mathematics

Algebraic Structure on the Euclidean Projective Line - Rational Geometry Math Foundations 137

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Explores algebraic structure on the Euclidean projective line, covering projective formulas, isometries, rotations, and their compositions. Connects to chaos theory and complex number multiplication.
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9 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Part 4

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Practical implementation of quaternions for 3D rotations, focusing on half-turns and vector trigonometry. Explores quaternion multiplication and its geometric interpretation for rotations.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Insights into Mathematics

Commutative Groups: Isomorphisms, Homomorphisms, Cosets and Quotient Groups - Lecture 3

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Explore commutative groups, isomorphisms, homomorphisms, cosets, and quotient groups. Learn the fundamental structure theorem and its applications in understanding group theory concepts.
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1 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

Lattice Relations and Hermite Normal Form - Abstract Algebra Math Foundations 224

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Explore lattices and integral linear spans of vexels, including the Hermite normal form algorithm for understanding lattice structure and relations between elements in a spanning set.
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1 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Challenges in Abstract Algebra - Math Foundations 214

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Explores logical difficulties in abstract algebra, focusing on defining groups and the impact of different definitions on group theory development. Emphasizes critical thinking in mathematical foundations.
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1 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Reciprocals, Powers of 10, and Euler's Totient Function - Math Foundations 202

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Explore decimal expansions of fractions, their connection to modular arithmetic, and Euler's totient function. Gain insights into repeated decimal cycles and their relationship with powers of 10 mod n.
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1 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers, Polynumbers and Arithmetic with Vexels - Data Structures Math Foundations 190

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Exploring Hindu Arabic numerals through multiset orientation, polynumbers, and vexels. Connects algebra and arithmetic concepts for a deeper understanding of number systems.
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9 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Difficulties with Cyclotomic Fields - Famous Math Problems 20

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Explores logical issues in cyclotomic fields, focusing on the challenges of embedding roots of unity into complex numbers and the limitations of purely algebraic approaches.
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1 Lesons
29 minutes
On-Demand
Free-Video
IMSA

Basics in Commutative Algebra - January 29, 2024

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Explore fundamental concepts of commutative algebra, focusing on face rings and the Ishida complex, with insights into their algebraic properties and applications.
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1 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Combinatorial Conjectures and Algebraic Tools - January 30, 2024

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Explore combinatorial conjectures like Grünbaum and g-conjectures, and their connections to deeper algebraic properties in this insightful overview.
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1 Lesons
51 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Complex Surfaces With Many Algebraic Structures

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Explore complex surfaces with multiple algebraic structures through blowups, elliptic curves, and Hopf transforms. Discover new insights in algebraic geometry and complex analysis.
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1 Lesons
1 hour 5 minutes
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Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Delannoy Category - Symmetric Tensor Categories and Representation Theory

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Explore the Delannoy Category in symmetric tensor theory, featuring classification of simple objects, tensor product rules, and a combinatorial model using Delannoy paths.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Nil-Brauer Category - Categorification and Applications

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Exploration of the nil-Brauer category, its relation to quantum groups, and applications in categorification and Soergel bimodules, presented by Jonathan Brundan at IPAM's workshop.
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1 Lesons
54 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Low Rank Symmetric Fusion Categories in Positive Characteristic

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Explore classification of symmetric fusion categories in positive characteristic, focusing on low-rank cases and the second Adams operation's role in obtaining classification results.
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1 Lesons
30 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Tannakian Radical and Mantle of a Braided Fusion Category

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Explore Tannakian radical and mantle concepts in braided fusion categories, their properties, and applications in classification theory with mathematician Dmitri Nikshych.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Extended Freudenthal Magic Square via Tensor Categories

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Explore unital composition superalgebras and their connection to the Extended Freudenthal Magic Square in characteristic 3, using symmetric tensor categories and representation theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Polynomial Superfunctors - Applications to Finite Supergroup Schemes

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Explore polynomial superfunctors and their applications in finite supergroup schemes. Gain insights into cohomology calculations and recent developments in representation theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Growth and Tensor Products in Representation Theory - Lecture 1

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Explore asymptotic counting of summands in tensor products of representations, with numerous examples to illustrate concepts in symmetric tensor categories and representation theory.
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1 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Positivity and Higher Teichmüller Spaces

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Explore positivity in Lie groups, positive representations, and their connected components. Delve into Hitchin's Teichmüller components and related open questions in higher Teichmüller theory.
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1 Lesons
1 hour
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

On the Geometry of Uniform Meandric Systems

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Exploring the geometry of meandric systems, focusing on a century-old question about loop crossings. Presents a conjecture on large-scale geometry and related rigorous results.
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1 Lesons
55 minutes
On-Demand
Free-Video