Pathways Workshop: Representation Theory Under the Influence of Quantum Field Theory & Motivic Homotopy Theory: Recent developments in equivariantly enriched enumerative geometry
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
This talk will be an accessible survey of recent developments equivariantly enriched enumerative geometry, a research program that aims to study classical enumerative problems under the presence of a finite group action to count orbits of solutions. I will give motivation, examples of questions one can ask in this field, and examples of theorems answering them. No prior knowledge of enumerative geometry or equivariant homotopy theory will be assumed. Results I will mention are joint with Thomas Brazelton, Kirsten Wickelgren, and Charanya Ravi.