Research

My research interests are symplectic topology, contact topology and dynamics. Now I am focusing on the following projects:

• Study Hofer geometry and spectral geometry from a large scale perspective
• Detect various phenomena in symplectic(contact) topology and dynamics via quantitative method
• Use recent-developed global Kuranishi techniques to study symplectic(contact) geometry
• Derive quantitative invariants(e.g. spectral invariants, barcodes, barcode entropy) from various homologies(e.g. Hamiltonian Floer homology, Rabinowitz Floer homology, Embedded contact homology)
• Discover connections between symplectic geometry and algebraic geometry

The followings are some research writings(drafts).

• Various measurements on the space of contact forms
• Superheaviness result on the skeleton of divisor complement
• Linked twisted maps and Hofer distance
• Barcode entropy and embedded contact homology
• Quantities from $S^1$-equivariant Rabinowitz Floer homology
• Open string symplectically degenerate minimum and relative Poincare-Birkhoff theorem
• Equivariant Floer theory via global Kuranishi charts and the Hofer-Zehnder conjecture, joint with Jun Zhang, in progress
• A relative monopole Floer theory and Legendrian embedded contact homology, in progress