A copy of my research statement is here.
My research is primarily concerned with topology of three-manifolds. In particular, my interests include:
Knot theory,
Surfaces in three-manifolds, including Heegaard splittings,
Combinatorial approaches to three-manifolds,
The arc-and-curve complex of surfaces.
My writings so far are listed below.
Heegaard genus and complexity of fibered knots, Journal of Topology 15 (2022), 2389-2425: A comparison of Heegaard splittings and fibered knots in closed three-manifolds, using thin position arguments, yields that a sufficiently complicated fibered knot induces the minimal genus Heegaard splitting.
Non-prime three-manifolds with open book genus two, (2017): A classification of non-prime three-manifolds that have genus two Heegaard splittings induced by fibered links.
 A survey of three-manifolds, (2017): A survey of classical results in the three-manifolds literature, which I wrote for my comprehensive exam. I hope the survey can be helpful for younger graduate students who are planning to study three-manifolds. Any comments and corrections are welcome.
Aside from these, I enjoy reading and thinking about the Cabling Conjecture and the Berge Conjecture, which assert classifications of knots in the three-sphere that admit special surgeries. Information about these problems can be found in the survey above.
My favourite statements in the three-manifolds literature are the following:
Jaco's handle addition lemma (1984), which states that handle attachment to a compressible boundary along a disk-busting curve yields incompressible boundary.
Casson-Gordon's reducing Heegaard splittings theorem (1987), which states that a weakly reducible Heegaard splitting, which is not reducible, can be compressed to an incompressible surface.