Linear Algebra
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.
Commutative Algebra
Comprehensive exploration of commutative algebra concepts through 60 lectures, covering fundamental principles and advanced topics for a deep understanding of algebraic structures.
Computation as Semigroups, Computing Semigroups
Explore the intersection of semigroups, computation, and functional programming. Gain insights into mathematical foundations of software engineering from a unique perspective.
Algebraic Structure of Area-Preserving Homeomorphism Groups - Lecture 4
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.
On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 2
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.
On the Algebraic Structure of Groups of Area-Preserving Homeomorphisms - Lecture 1
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.
Group Theory
Comprehensive exploration of group theory, covering key concepts from basic definitions to advanced topics like Sylow theorems, ideal for mathematics and engineering students.
Introduction to Quantized Enveloping Algebras - Leonardo Maltoni
Explore quantized enveloping algebras, their structure, and applications in quantum groups. Learn about Gaussian binomial coefficients, q-deformations, and Hopf algebra structures.
An Introduction to Geometry and Dynamics on Semisimple Lie Groups - Part 1
Explore semisimple Lie groups, their structure, discrete subgroups, and asymptotic behavior in this comprehensive introduction to geometry and dynamics.
Substitutions in Non-Commutative Multivariate Power Series
Explore group laws on non-commutative formal power series, their structures, and applications in non-commutative probability theory through a Hopf algebraic approach.
Hidden Symmetries in Fluid Dynamics - Lecture 8
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.
Hidden Symmetries in Fluid Dynamics - Lecture 7
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.
Hidden Symmetries in Fluid Dynamics - Lecture 5
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.
Hidden Symmetries in Fluid Dynamics - Lecture 4
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.
Equações de Grau Cinco
Explore a complexidade das equações de grau cinco e suas soluções, aprofundando-se em conceitos matemáticos avançados e suas implicações teóricas.
Categorification at Roots of Unity
Explorez la catégorification des groupes quantiques aux racines de l'unité, en examinant les algèbres p-DG et les représentations catégoriques pour sl(2).
Spaces of Orderings and Applications - Lecture 4
Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
Spaces of Orderings and Applications - Lecture 3
Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
Spaces of Orderings and Applications - Lecture 1
Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
R-matrices for the Category O of Quantum Loop Algebras
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.
Contando Cuerpos de Números Algebraicos
Explora la teoría de cuerpos de números algebraicos y sus aplicaciones en matemáticas avanzadas. Profundiza en conceptos fundamentales y técnicas de conteo.