My research lies in low-dimensional topology, contact geometry, and knot theory. In particular, I am interested in classification and structural problems involving Legendrian and transverse knots using tools from Heegaard Floer homology and Khovanov homology.

One of the central questions motivating my research is: What information is needed to completely classify Legendrian and transverse knots? Unlike smooth knot theory, the presence of a contact structure imposes additional geometric constraints on knots. Although certain knot types are completely classified by their classical invariants, there are many examples of Legendrian and transverse knots that cannot be distinguished by these invariants alone. This motivates the development of finer invariants, particularly those arising from knot Floer homology and Khovanov homology.

A central theme of my work is constructing and understanding transverse knot invariants through cyclic branched covers and stable homotopy refinements of Khovanov homology. I am also interested in understanding how Legendrian and transverse knots behave under covering maps, and whether the invariants of their lifts can provide additional information about the original knots.

Some broader questions that interest me are:

• How can we construct more effective invariants for distinguishing Legendrian and transverse knots?

• What information about a transverse knot is captured by its cyclic branched covers and the lifted knots?

• How do Legendrian and transverse invariants behave under covering maps, and what information is preserved or lost?

• Can the relationships between knot Floer homology and Khovanov homology provide new transverse invariants?