Langlands Duality for the Affine Hecke Category
Explore Langlands duality for affine Hecke category, its applications in representation theory, and potential generalizations to symplectic singularities. Gain insights into geometric local Langlands duality.
Stationary Measures for Integrable Probabilistic Systems
Explore advanced mathematical concepts in integrable probabilistic systems, focusing on stationary measures, discrete models, and their applications in theoretical physics and mathematics.
Colored Vertex Models, Orthogonal Functions and Probability - Lecture 2
Delve into advanced concepts of colored vertex models, exploring their connections to orthogonal functions and probability theory through expert mathematical analysis and demonstrations.
Peng Shan- On Geometrical Realization of Centers
Explore connections between algebra centers and geometric cohomology, focusing on quantum groups and affine Springer fibers in Lie theory.
Crystal Bases for Quantum Superalgebras - Lecture 2
Explore crystal bases for quantum superalgebras, focusing on advanced representation theory concepts and their applications in mathematical physics.
Floer Theory and Quantum Groups
Explore Floer theory, quantum groups, and gauge theories in 3-manifolds. Discover connections between moduli spaces, Floer invariants, and skein modules in topological quantum field theory.
Unifying Lattices Through Hourglass Plabic Graphs
Explore connections between web bases, quantum groups, and lattice models. Discover new combinatorial frameworks linking alternating sign matrices, plane partitions, and the Tamari lattice.
Universality of Dynamic Processes Using Drinfel'd Twisters
Explore universality in dynamic processes using Drinfel'd twisters, examining long-time asymptotics and Tracy-Widom fluctuations through quantum group duality and asymptotic analysis.
Tracial and G-invariant States on Quantum Groups
Explore tracial and G-invariant states on quantum groups, examining connections between traceability and G-invariance in discrete quantum group C*-algebras.
New Applications of the Reflection Equation Algebras
Explore new applications of Reflection Equation Algebras, including q-analogs of Schur-Weyl duality, Capelli formula, and Frobenius formula in quantum mathematics.
Categorified Crystal Bases on Localized Quantum Coordinate Rings
Explore categorified crystal bases on localized quantum coordinate rings, focusing on monoidal categories, quiver Hecke algebras, and crystal structures in quantum algebra.
Cohomological Hall Algebras of Zero-Dimensional Sheaves on Surfaces and the P=W Conjecture
Explore cohomological Hall algebras of 2CY categories, focusing on zero-dimensional sheaves on surfaces and their role in proving the P=W conjecture for character varieties.
Infinite-Dimensional Spin Chains from Gauge Theory
Explore infinite-dimensional spin chains in gauge theory, connecting quantum mechanics, particle physics, and mathematics through innovative approaches to Bethe ansatz and Langlands programs.
Non-semisimple TQFTs from 3D N=4 Quantum Field Theories - Part 1
Explore non-semisimple TQFTs from 3D supersymmetric field theories, examining their connections to quantum groups and vertex operator algebras in topological quantum field theory.
Cluster Nature of Quantum Groups
Explore quantum groups through a rigid cluster model, discovering natural Hopf algebra isomorphisms and a cluster canonical basis with unique invariance properties.
Introduction to Quantum Integrability - Lecture 1
Explore quantum integrability fundamentals with Jules Lamers in this comprehensive lecture, part of a five-part series delving into advanced concepts and applications.
Introduction to Quantum Integrability - Lecture 1
Explore quantum integrability fundamentals, focusing on key concepts and applications in theoretical physics.
Integrability of Box-Ball Systems and Randomized Box-Ball Systems - Part 1
Explorez l'intégrabilité des systèmes de boîtes à boules et leurs versions aléatoires. Découvrez les liens avec la théorie des cristaux, l'ansatz de Bethe et l'ultradiscrétisation dans ce domaine fascinant des mathématiques.
Belavin-Drinfeld Quantum Groups - Survey and Future Directions
Explore Belavin-Drinfeld quantum groups, their deformations, and connections to semi-simple algebraic Poisson groups. Survey current knowledge, conjectures, and future research directions in this field.
Modular Tensor Categories, Quantum Groups and Vertex Algebras - Lecture 4
Explore connections between modular tensor categories, quantum groups, and vertex algebras. Delve into the logarithmic Kazhdan–Lusztig conjecture linking quantum groups and vertex algebras.
Fermionic Forms in Logarithmic Vertex Operator Algebras and BPS Quivers
Explore connections between quantum groups, vertex algebras, and quiver representations. Uncover new insights into fermionic forms and their applications in representation theory and enumerative geometry.