Pathways Workshop: Representation Theory Under the Influence of Quantum Field Theory & Motivic Homotopy Theory: Homological Mirror symmetry and Quantum Groups
August 20, 2026
Keywords:
- Coulomb branches
- symplectic duality
- 3d mirror symmetry
- geometric Langlands program
- geometric representation theory
- supersymmetric gauge theories
- TQFT
- Motivic homotopy theory
- (algebraic) vector bundles
- stable homotopy groups of spheres
- affine algebraic varieties
MSC:
- 14F42 - Motivic cohomology
- motivic homotopy theory
- 19E15 - Algebraic cycles and motivic cohomology KK-theoretic aspects
- 14N15 - Classical problems Schubert calculus
- 22E46 - Semisimple Lie groups and their representations
- 22E57 - Geometric Langlands program representation-theoretic aspects
- 22E50 - Representations of Lie and linear algebraic groups over local fields
- 14D21 - Applications of vector bundles and moduli spaces in mathematical physics twistor theory instantons
- quantum field theory
- 81T13 - Yang-Mills and other gauge theories in quantum field theory
- 57K16 - Finite-type and quantum invariants
- topological quantum field theories
- 53D55 - Deformation quantization star products
- 14J33 - Mirror symmetry algebro-geometric aspects
Abstract
There is a new family of homological mirror pairs for which homological mirror symmetry can be understood as explicitly as in the simplest known examples. The resulting categories categorify braid-group representations coming from quantum groups. One application is the categorification of quantum link invariants. Another is a solution to an outstanding problem in higher representation theory: describing a categorification of the Hopf algebra structure of a quantum group.