I am interested in studying the geometry of mapping class groups of non-orientable surfaces and their subgroups using tools from geometric group theory.

Much work has been done to understand the mapping class group of a finite-type orientable surface, but much remains to be discovered about the other cases. During my Ph.D. studies, I extended this research to the finite-type non-orientable case, and I fell in love with non-orientable surfaces. I am also interested in the infinite-type case and how Geometric Group Theory can be used to study it. I am fascinated by the fact that some mathematical areas that I thought were far removed from this, such as set theory, appear naturally. 

Hyperbolicity is one of my favorite group properties. I'm always looking to study groups that behave in this manner, and I love seeing the generalizations of hyperbolicity that can be achieved by thinking about it. Specifically, I am interested in relative hyperbolicity, hierarchically hyperbolic spaces, and coarse median spaces.

Recently, I have developed an interest in cryptography. I am still learning, but I am interested in learning about the applications of geometric group theory to the development of cryptosystems.