# Mathematical Interests

## 1. Lie Theory

*Short-term interests (ready to tackle!):*

- Clebsch–Gordan coefficients for SU(2)
- Weights, root systems and the Weyl group, especially in the context of SU(3)
- Curvature of Lie groups

*Long-term interests (curious, but need a stronger foundation first):*

## 2. Representation Theory

*Short-term interests:*

- Combinatorial aspects of representation theory of the symmetric group
- The Haar measure and its role in the representation theory of compact Lie groups
- Applications to point group determination in chemistry
- Quivers

*Long-term interests:*

- Representations of Hopf algebras and quantum groups

## 3. Knot Theory

*Short-term interests:*

- Seifert surfaces
- Keis and quandles
- Khovanov homology

*Long-term interests:*

- The connection between the Jones polynomial and quantum groups

## 4. Topology

*Short-term interests:*

- Differential topology
- The topology of order complexes
- Topological data analysis
- Spectral sequences

*Long-term interests:*

- Morse theory
- K-theory
- Characteristic classes

## 5. Geometry

*Short-term interests:*

- Differential forms
- Curvature and geodesics on Lie groups
- Geometric group theory

*Long-term interests:*

- De Rham cohomology
- Exotic spheres
- Symplectic geometry
- Teichmüller theory