Research

My research is centered around the moduli of vector bundles, generally on curves. Some buzz words include Bun_G, loop groups, affine Grassmannian, toric varieties, (gauged) Gromov-Witten theory, vector bundles on projective space and monads. I'm particularly interested in the wonderful compactification of an adjoint group. In my thesis I constructed a loop group version of the
wonderful compactification and used it to study degenerations of Bun_G to nodal curves.

### Papers

- Natural Cohomology on P1 x P1
- Hunting Bundles on P1 x P1
- Infinite type toric varieties and Voronoi Tilings
- Nodal Uniformization of G-bundles
- Stable gauged maps

(joint with E. Gonzalez, C. Woodward) - Properness for scaled gauged maps

(joint with E. Gonzalez, C. Woodward) - A Wonderful Embedding of the Loop Group
- A complete degeneration of the moduli of G-bundles on a curve

As an undergraduate I worked on a project in knot theory. I wrote the following papers

- On the Harary-Kauffman conjecture and Turk's head knots.

(Joint with Dowdall, Mattman, Meek ) - A proof of the Kauffman-Harary conjecture

(joint with Mattman)