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 Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators
Explore Loop Braid Group, Loop Hecke Algebras, and charge conserving Yang-Baxter operators. Gain insights into recent mathematical developments in quantum symmetries and topological quantum field theories.
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.
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.
Affine W-algebras - Lecture 3
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Lecture 2
Explore affine W-algebras through quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
Real Groups, Symmetric Varieties and Langlands Duality - ICBS 2024
Explore connections between relative Langlands duality and geometric Langlands for real groups, examining derived Satake equivalence for symmetric varieties.
Recent Progress in Geometric Langlands - ICBS 2024
Explore recent advancements in geometric Langlands theory, including verified conjectures and related questions in algebraic geometry and representation theory.
On the p-adic Local Langlands Correspondence
Explore the $p$-adic local Langlands correspondence for ${\mathrm GL}_2({\mathbb Q}_p)$, focusing on geometric constructions from joint works with Dospinescu and Niziol.
Homological Aspects of Branching Laws in p-adic Groups
Explore homological aspects of branching laws for p-adic group representations, focusing on restriction to subgroups and projective representations in Bernstein blocks.
Growth in Tensor Powers
Explore tensor power decomposition in group representations, focusing on asymptotic behavior and non-negligible summands using symmetric tensor category theory.
Higher Auslander Algebras and Higher Representation Finite Algebras
Explore higher Auslander algebras, their construction methods, and connections to representation theory. Gain insights into recent developments and applications in algebra and representation theory.
Higher Order KR-Modules, Imaginary Modules and Monoidal Categorification
Explore connections between cluster algebras, quantum affine algebras, imaginary modules, and representation theory of general linear groups over non-archimedean fields.
Embeddings of Kac-Moody Affine Grassmannian Slices
Explorez les développements récents dans la théorie des représentations géométriques, en se concentrant sur les tranches de Grassmanniennes affines de type Kac-Moody et leur construction via les branches de Coulomb.
T-Shift on Reduced Plabic Graphs and Legendrian Weaves
Explorez les T-shifts sur les graphes plabiques réduits et les tissages légendrien pour interpréter topologiquement la structure de cluster des strates positroïdes du grassmannien.
Newton-Okounkov Bodies and Minimal Models for Cluster Varieties
Explore Newton-Okounkov bodies construction for line bundles on cluster variety minimal models, with applications to Grassmannians and flag varieties. Examine connections to representation theory polytopes.
Parabolic Hilbert Schemes and Rational Cherednik Algebras
Explore connections between symmetric group representations, rational Cherednik algebras, and parabolic Hilbert schemes. Gain insights into geometric constructions of irreducible modules using combinatorics and torus fixed points.
Similarities Between Representation Theories of Finite Groups in Positive Characteristic and Algebraic Supergroups
Explore similarities between representation theories of finite groups in positive characteristics and algebraic supergroups, including Sylow subgroups and Green correspondence for supergroups.
Monoidal Triangular Geometry with Applications to Representation Theory
Explorez la géométrie triangulaire monoïdale et ses applications à la théorie des représentations, en mettant l'accent sur les algèbres de Hopf de dimension finie et les catégories tensorielles finies.
Spherical Functions and Mirror Symmetry
Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.