I’m currently a Benjamin Peirce Fellow at Harvard Math Department. My mentor is Peter Kronheimer. I finished my Ph.D. program in Maths at University of Cambridge and my supervisor is Jacob RasmussenHere is my complete CV.

I’m interested in low-dimensional topology, especially gauge theory (instanton, monopole, Heegaard Floer homology) and knot polynomials (Khovanov homology, sl_n homology, HOMFLY-PT polynomial). I’m also interested in symplectic geometry and mathematical physics.

Peter Kronheimer and I organize the Gauge theory and Topology seminar this fall.

I teach Math230A: Differential Geometry this fall.

Research

[1] Knot surgery formulae for instanton Floer homology II: applications
Joint with Zhenkun Li, submitted, arXiv:2209.11018 || PDF

[2] Seifert surface complements of nearly fibered knots
Joint with Zhenkun Li, submitted, arXiv:2208.05382 || PDF

[3] Knot surgery formulae for instanton Floer homology I: the main theorem
Joint with Zhenkun Li, submitted, arXiv:2206.10077 || PDF

[4] Small Dehn surgery and SU(2)
Joint with John A. Baldwin, Zhenkun Li, and Steven Sivek, accepted by Geometry & Topology, arXiv:2110.02874 || PDF

[5] SU(2) representations and a large surgery formula
Joint with Zhenkun Li, submitted, arXiv:2107.11005 || PDF || Talk || Slides

[6] An enhanced Euler characteristic of sutured instanton homology
Joint with Zhenkun Li, submitted, arXiv:2107.10490 || PDF

[7] Instanton Floer homology, sutures, and Euler characteristics
Joint with Zhenkun Li, accepted by Quantum Topology, arXiv:2101.05169 || PDF || Talk, Part IPart II || Slides

[8] Sutured instanton homology and Heegaard diagrams
Joint with John A. Baldwin and Zhenkun Li, submitted, arXiv:2011.09424 || PDF

[9] Instanton Floer homology, sutures, and Heegaard diagrams
Joint with Zhenkun Li, Journal of Topology 15 (1): 39-107 (2022), DOI:10.1112/topo.12218 || arXiv:2010.07836 || PDF || Talk by Zhenkun Li

[10] Constrained knots in lens spaces
Accepted by Algebraic & Geometric Topology, arXiv:2007.04237 || PDF || List of constrained knots || Data || Talk || Slides || Poster

Ph.D. Thesis, New techniques in calculation of sutured instanton Floer homology:
by Heegaard diagrams, Euler characteristics, and Dehn surgery formulae, DOI: 10.17863/CAM.85094 || PDF

 

Conferences and Talks

 

Updated in Sept 2022