My primary research interests are arithmetic geometry and non-commutative algebra. In my research I have used field patching techniques and generic Galois theory to construct division algebras with certain Galois maximal subfields over semi-global fields (function fields of curves over complete discretely valued fields). Field patching is a powerful tool which can be used to build algebraic structures over these fields by patching together compatible structures over a carefully chosen system of their overfields.
I am currently in the process of writing-up the results from this project for publication. I have given talks on my research and related background topics, some of which were recorded.