My primary research interests are in the areas of metric number theory and homogeneous dynamics. Metric number theory is concerned with describing the size of sets of numbers which satisfy certain number theoretic properties. Often, these properties concern how well the numbers can be approximated either by rational numbers, or some other dense subset of the real numbers. These questions have a surprising but beautiful connection with homogeneous dynamics. The result being that studying the ergodic properties of transformations on homogeneous spaces and shrinking target problems in those settings can answer questions about the size of sets which satisfy approximation restrictions.
I additionally have been exploring answering questions about chess through a mathematical lens. For example, questions about how the knights move on the chess board, and if a knight can be contained in some way, can be answered by examining properties of the resulting knight's graph, and subgraphs thereof.