Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part I
Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial definitions, enhancing understanding of statistical mechanics and representation theory.
The Origin of Trigonometric K-matrices - Part I
Explore the mathematical foundations of quantum integrability with boundaries, focusing on K-matrices and their universal properties in relation to quantum affine algebras and reflection equations.
Integrability of Box-Ball Systems and Randomized Box-Ball Systems - Part II
Explore integrability and randomization in box-ball systems. Delve into crystals, Bethe ansatz, ultradiscretization, and analytical results from TBA and GHD. Gain insights into density plateaux and current correlations.
Riesz Inequality for Polygons: Symmetry and Symmetry Breaking
Explore counterparts of Hardy-Littlewood and Riesz inequalities for polygons, examining symmetry and symmetry breaking in nonlocal isoperimetric problems.
Aggregation-Diffusion and Kinetic PDEs for Collective Behavior: Applications in Sciences
Explorez les modèles mathématiques de comportement collectif, leurs propriétés et applications en biologie et ingénierie. Découvrez les phénomènes de ségrégation, transitions de phase et consensus.
Extensions of Affine Algebra Vertex Operator Algebras
Explore extensions of affine algebra VOAs, focusing on V(g,k) for simple Lie algebras. Learn about finite-index extensions, simple currents, and quantum subgroups in module category classification.
Extension of Bershadsky-Polyakov Type Algebras
Explore toroidal shifted algebras and deformed W-algebras, focusing on extensions of Bershadsky-Polyakov type algebras in quantum symmetries.
Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology
Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.
Volume Conjecture for Surface Diffeomorphisms
Explore quantum invariants for surface diffeomorphisms and their connection to mapping torus volume. Examine representation theory, numerical evidence, and a proof for the figure-eight knot complement case.
4D/2D Duality and Representation Theory in Quantum Field Theory
Explore the 4D/2D duality in superconformal field theory, connecting 4D theories to vertex operator algebras and examining their representation theory and symplectic singularities.
Diagrammatics in Categories - Lecture 4
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique. Développez votre compréhension des applications dans divers domaines.
Algebraization of Low-Dimensional Topology - Part II
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Diagrammatics in Categories - Lecture 5
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique, en laissant place à la généralisation.
Affine W-algebras - Lecture 5
Explore affine W-algebras construction, theory, and applications in vertex algebra. Delve into quantum Hamiltonian reduction, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Lecture 4
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Towards the Quantum Exceptional Series
Explore continuous families of planar algebras interpolating exceptional Lie algebras and their quantum counterparts. Discover a potential new exceptional knot polynomial through skein theoretic analysis.
Affine W-algebras - Part I
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
W-algebras and Lax Operators - Lecture 5
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
W-algebras and Lax Operators - Lecture 3
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
Mathematics and Machines: Navigating New Frontiers
Explore the intersection of mathematics and machine learning, examining how computers transform mathematical research and their potential future impact on the field.
Polyhedra with Vertices on a Quadric
Explore combinatorial types of polyhedra with vertices on quadrics, from Steiner's 1832 question to recent findings using ideal polyhedra in various geometries.