# 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

*Long-term interests:*

- Khovanov homology
- The connection between the Jones polynomial and quantum groups

## 4. Topology

*Short-term interests:*

- Cohomology
- CW-complexes
- Differential topology and fixed-point theorems
- The topology of order complexes
- Topological data analysis

*Long-term interests:*

- Morse theory
- Higher homotopy groups and fibrations

## 5. Geometry

*Short-term interests:*

- Differential forms
- More on the geometry of Lie groups, for example their curvature or geodesics
- Geometric group theory

*Long-term interests:*

- De Rham cohomology
- Exotic spheres
- Symplectic geometry