My work focuses on gauge theory, Floer homology and low-dimensional topology.
Lately I have been thinking about a Pin(2)-equivariant version of monopole Floer homology.
Here is the list of my works (with links to arXiv when available):
- Pin(2)-monopole Floer homology and the Rokhlin invariant - submitted.
- Monopole Floer homology and the spectral geometry of three-manifolds - submitted.
- Bar Natan's deformation of Khovanov homology and involutive monopole Floer homology. - submitted.
- Pin(2)-monopole Floer homology, higher compositions and connected sums - to appear in Journal of Topology.
- The surgery exact triangle in Pin(2)-monopole Floer homology - Algebraic & Geometric Topology 17-5 (2017), 2915--2960.
- A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture - to appear in the Memoirs of the AMS.
- Exact Lagrangian caps of Legendrian knots - Journal of Symplectic Geometry, Vol. 14, No. 1 (2016), pp. 269-295.
Some expository writings:
- In Spring 2018, I am teaching MAT 202 Linear Algebra with Applications.
- In Fall 2017, I taught the Junior Seminar in Geometry. The topic was Differential Topology, and the main references Milnor's books Topology from the differentiable viewpoint and Morse theory.