# Mathematical Interests

(mostly just a long list of things that I want to learn more about)

## Combinatorial and computational algebraic geometry

- GrÃ¶bner bases
- Toric geometry
- Tropical geometry
- Polyhedral geometry
- Matroids
- Homotopy continuation
- Intersection theory and Schubert calculus
- Cluster algebras
- Connections to representation theory

## Applied algebra, geometry and topology

- Chemical reaction networks
- Algebraic statistics (especially in the context of phylogenetics)
- Algebraic methods in image analysis
- Sampling of varieties
- Persistent homology
- Point group determination in chemistry

## Other (currently less active) mathematical interests

*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
- Keis, quandles and racks

*Representation theory:*

- Lie groups and Lie algebras
- Quantum groups and Hopf algebras
- Quiver representations

*Algebraic topology:*

- Operads
- Cobordism groups
- Higher-dimensional TQFTs
- Characteristic classes
- Mapping class groups