# Mathematical Interests

(currently just a giant list of things that I want to learn more about)

## Applied and computational algebra

- Gröbner bases
- Toric and tropical geometry
- Connections to combinatorics and polyhedral geometry
- Matroids
- Homotopy continuation
- Intersection theory and Schubert calculus
- Cluster algebras
- Chemical reaction networks
- Algebraic statistics (especially connections to phylogenetics)
- Algebraic methods in image analysis
- Sampling of varieties
- Algebro-geometric perspectives on persistent homology

## Knot theory

- Khovanov homology (and variations thereof: odd, unified, annular, Lee homology...)
- In particular: detection results, algorithms, spectral sequences, homology operations...
- Relations between Khovanov homology and Floer theory.
- Connections between the Jones polynomial (and Khovanov homology) and quantum groups
- Link concordance
- Hyperbolic knots
- Keis, quandles and racks

## Representation theory

- Quantum groups and Hopf algebras
- The Haar measure and its role in the representation theory of compact Lie groups
- The Peter–Weyl theorem
- Quiver representations and Gabriel's theorem
- Applications in algebraic combinatorics
- Applications to point group determination in chemistry

## Topology

*Algebraic topology:*

- Cobordism groups
- Higher-dimensional TQFTs
- K-theory
- Morse theory
- Characteristic classes
- Surgery
- Exotic spheres
- Teichmüller theory and the mapping class group