I am a Mathematical Physicist working on the boundary of theoretical physics and differential geometry. My research has mostly been related to field theories, particularly gauge theories which admit soliton solutions. I have also worked a little with the theory of synthetic gauge fields in ultracold atomic gasses. A recent theme of my research has involved finding and exploring solvable models of chiral magnets. Essentially I am interested in studying mathematical problems motivated by physical systems.
A soliton is a stable particle like lump of energy which does not dissipate over time. They appear in many areas of mathematics and physics including: models of the nuclei of atoms, vortices in superfluids and superconductors, magnetic skyrmions in chiral magnets, and instantons and magnetic monopoles in gauge theories. Often the study of solitons involves the application of interesting mathematical techniques from both differential geometry and analysis.