My work focuses on gauge theory, Floer homology and low-dimensional topology.
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
Accepted for publication in Communications in Analysis and Geometry.
- Bar-Natan's deformation of Khovanov homology and involutive monopole Floer homology.
Accepted for publication in Mathematische Annalen.
- 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 2019, I will teach a graduate class on gauge theory and low-dimensional topology
- 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.