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.
Liouville and JT Quantum Gravity - Holography and Matrix Models
Explore holography and matrix models in Liouville and JT quantum gravity, covering fixed-length boundaries, partition functions, multi-boundary amplitudes, and quantum group interpretations.
Noncommutative Geometry of Quantum Flag Manifolds
Explore noncommutative geometry and quantum flag manifolds in this advanced mathematics lecture, delving into complex algebraic structures and their applications.
A Álgebra de Nós
Explore a fascinante álgebra de nós com o pesquisador Jethro van Ekeren. Descubra como essa área da matemática conecta topologia e álgebra, revelando insights surpreendentes sobre estruturas geométricas.
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).
Weyl Algebras for Quantum Homogeneous Spaces and Applications
Explore quantum analogues of differential operators on symmetric spaces, examining Capelli operators and their connection to Macdonald polynomials in representation theory.
Vertex Algebras and Quantum Groups with Big Center
Explore vertex algebras and quantum groups with large centers, focusing on semisimple Lie algebras and their connections to quantum geometric Langlands correspondence and logarithmic Kazhdan-Lusztig conjecture.
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.
Braided Fusion Categories - Lecture 3
Explore semisimple braided tensor categories, their structure, and classification. Delve into centralizers, non-degeneracy, equivariantizations, and the core of braided fusion categories.
New Signed Bijections Pertaining to Alternating Sign Matrices and Gelfand-Tsetlin Patterns
Delve into advanced mathematical concepts exploring signed bijections, alternating sign matrices, and Gelfand-Tsetlin patterns through rigorous theoretical analysis and problem-solving approaches.
Cyclotomic KLR Algebras - Part 1 of 4
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.
Drinfeld Center, Tube Algebra, and Representation Theory of Monoidal Categories
Explore connections between category theory, subfactor theory, and quantum groups. Learn about Drinfeld center, tube algebra, and representation theory of monoidal categories.
Quivers, Curve Counting, and Fermionic Sums in Topology
Explore connections between quantum groups, vertex algebras, and quiver representations in topology. Discover how fermionic forms link these areas, shedding new light on enumerative geometry and curve counting.
Tony Feng- A New Approach to Breuil-Mezard Cycles
Explore a novel local and group-theoretic approach to the Breuil-Mezard Conjecture, connecting it to quantum groups and homological mirror symmetry in algebraic number theory.
Crossed Product Equivalence of Quantum Automorphism Groups
Explore quantum automorphism groups and their crossed product equivalence in this advanced mathematics talk by Michael Brannan from the University of Waterloo.
The Composition Tableau and Construction of the Canonical Weierstrass Section
Explore the composition tableau and canonical Weierstrass section construction in this advanced algebraic geometry lecture by Yasmine Fittouhi, part of a broader program on representation theory.
Representation Theory in Infinite-Dimensional Algebras
Explore advanced representation theory concepts in this talk by Deniz Kus, covering algebraic and combinatorial methods in infinite-dimensional Lie algebras and quantum groups.
A Braided Monoidal 2-Category via Soergel Bimodules
Explore braided monoidal 2-categories through Soergel bimodules, examining quantum group representations and categorification in relation to Hecke algebras and quantum link invariants.
The Nil-Brauer Category - Categorification and Applications
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.
Quivers and Cohomological Hall Algebras - Lecture 3
Explore advanced concepts in quiver theory and cohomological Hall algebras, delving into complex mathematical structures and their applications in algebraic geometry.
Quivers and Cohomological Hall Algebras - Lecture 2
Explore advanced concepts in quiver theory and cohomological Hall algebras, delving into their intricate connections and applications in algebraic geometry and representation theory.