I'm interested in Differential Geometry and its applications to General Relativity. Most recently, I've been studying the effects of dark matter modeled as a scalar field. In particular, using the Einstein-Klein-Gordon equations to describe geometrically a general blob of dark matter and comparing this description to observations of Dwarf Spheroidal Galaxies, one of the smallest observed types of gravitationally bound objects that have a significant presence of dark matter.
In the past, I have studied Lie Algebras, in particular classifying solvable Lie algebras of small dimension. My master's thesis was on classifying such Lie algebras through dimension seven.