My research lies at the intersection of homogeneous dynamics, the study of group actions on homogeneous spaces, and number theory, more specifi- cally Diophantine approximation. The interplay between these two subjects has been playing a significant role in the wider mathematical landscape for several decades.
In this talk I aim to give a broad-brush picture of this area and and to describe a few of my on-going projects. By the end of the talk I will present to the audience some of the open questions and problems that motivate my future research, providing details if time permits.