This is a page about what I think.
I am broadly interested in low dimensional topology and geometry. My current research involves Riemann surfaces, hyperbolic geometry and Teichmuller theory. My main motivation for doing mathematics is pictures and visualizations so I love anything with pictures!
We look at filling closed curves on hyperbolic surfaces and consider its length infima over the Teichmuller space of the surface. In particular explore relations between this infimum and self-intersection number of curves. We construct curves with same intersection number but different length infimum.
This is joint work in progress with my advisor Ara Basmajian . Here are my slides from a talk I gave on my work. Also a postcard I made for a conference at ICERM.
For my masters thesis I studied relations between contact structures and co-dimension one foliations on 3-manifolds via open book decomposions. Here are slides from my thesis defense. Thesis: Codimension one foliations related to contact topology in low-dimensional manifolds via Open Books. Advisor: Joan Licata , Australian National University