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.
- 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 - to appear in Algebraic & Geometric Topology.
- 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 Fall 2017, I am teaching the Junior Seminar in Geometry. The topic will be Differential Topology.