Symmetries and Quantum Mechanics - Linear Representations
Explore the fundamental principles of group representation theory and its applications in quantum mechanics, focusing on linear representations and their mathematical foundations.
Symmetries and Quantum Mechanics - Basics, Wigner's Theorem, and Linear Representations of Groups
Explore the fundamental connection between symmetry and quantum mechanics through group representation theory, focusing on Wigner's theorem and its implications for physical systems.
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.
Monogamy of Highly Symmetric States in Quantum Entanglement
Explore entanglement limits in highly symmetric quantum states on complete graphs, using semidefinite programming and representation theory to solve long-standing problems.
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.
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.
Fock Spaces Associated with Coxeter Groups of Type B
Explore Fock spaces related to infinite hyperoctahedral groups, examining two-parameter functions and their positive definiteness in extreme characters. Apply findings to cyclic Fock spaces of type B.
Gauge Origami and Quiver W-algebras
Explore gauge origami and quiver W-algebras with Taro Kimura, delving into advanced mathematical concepts and their applications in theoretical physics.
Quantum Spin Chains and Symmetric Functions: Connections to Representation Theory and Combinatorics
Explore quantum spin chains' connections to representation theory, combinatorics, and algebraic geometry through quantum integrability and symmetric functions.
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.
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.
Braided Fusion Categories - Lecture 1
Explore semisimple braided tensor categories, their structure, and classification. Learn about centralizers, non-degeneracy, equivariantizations, gauging, and Witt equivalence in fusion categories.
Quantum Analytic Langlands - Quantisation of Moduli Spaces
Explore quantisation of moduli spaces through diverse perspectives, delving into the intricacies of Quantum Analytic Langlands theory.
The Center of the Small Quantum Group and Affine Springer Fibers
Explore representation theory through quantum groups and affine Springer fibers, focusing on the center of small quantum groups.
Spark Algebras and Quantum Groups
Explore representation theory through spark algebras and quantum groups, focusing on quantum topology concepts.
Bordered-Sutured Floer Homology as a Sutured TQFT
Explore advanced quantum topology concepts through bordered-sutured Floer homology and its applications as a sutured TQFT in this in-depth lecture by J. Rasmussen.
Heisenberg Homologies of Configurations in Ribbon Graphs
Explore Heisenberg homologies in ribbon graffs configurations, focusing on quantum topology and representation theory.
Non-semisimple Link and Manifold Invariants
Explore non-semisimple link and manifold invariants in quantum topology, focusing on representation theory with A. Gainutdinov from CNRS, Université de Tours.
Сагайдачні многовиди - Лекція 1
Dive into the mathematical world of Nakajima quiver varieties, exploring their construction, relationship with self-duality equations, and examining the Grassmannian example in theoretical physics.
One Clean Qubit Suffices for Quantum Communication Advantage
Delve into groundbreaking research demonstrating how a single clean qubit enables quantum communication advantage, challenging previous assumptions about quantum versus classical communication complexity.