My research interests lie mainly in the fields of differential geometry and geometric analysis. 
Geometric analysis is an active domain of mathematics situated at the interface between geometry, analysis and topology.

This topic concerns the study of geometric structures arising from Riemannian geometry, such as Einstein and soliton structures, and their uniformization using techniques of analysis. There are many interesting applications in Physics, for example in general relativity and elasticity theory. 
I am particularly interested in so-called soliton solutions of the Ricci flow, corresponding to metrics that evolve by rescaling and coordinate change under the flow. These solutions give a natural generalization of the Einstein condition and are also very important in the understanding of singularities of the Ricci flow via rescaling of variables.
Another interesting topic is harmonic maps, and harmonic morphisms. This field is a fascinating focal point for differential geometry, analysis, topology, algebra and even probability theory and hydrodynamics.