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 Rasmussen. Here 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, Josh Wang, and I organize the Gauge theory and Topology seminar this spring.
I will 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] The guts 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 Geom. Topol., 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, Int. Math. Res. Not. 2023, rnad066. doi:10.1093/imrn/rnad066 || arXiv:2107.10490 || PDF
[7] Instanton Floer homology, sutures, and Euler characteristics
Joint with Zhenkun Li, Quantum Topol. 14 (2): 201–284 (2023). doi: 10.4171/QT/182 || arXiv:2101.05169 || PDF || Talk, Part I, Part II || Slides
[8] Sutured instanton homology and Heegaard diagrams
Joint with John A. Baldwin and Zhenkun Li, Compos. Math. 159(9): 1898-1915 (2023). doi:10.1112/S0010437X23007303 || arXiv:2011.09424 || PDF || Talk by Zhenkun Li
[9] Instanton Floer homology, sutures, and Heegaard diagrams
Joint with Zhenkun Li, J. Topol. 15 (1): 39-107 (2022). doi:10.1112/topo.12218 || arXiv:2010.07836 || PDF || Talk by Zhenkun Li
[10] Constrained knots in lens spaces
Algebraic Geom. Topol. 23 (3): 1097–1166 (2023). doi: 10.2140/agt.2023.23.1097, 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
- Seminar Talk, UIUC, 10/2023.
- Seminar Talk, Boston College, 09/2023.
- Seminar Talk, Harvard, 09/2023.
- Seminar Talk, Academy of Mathematics and Systems Science, CAS, Beijing, 07/2023.
- Seminar Talk, Institute of Mathematics of the Polish Academy of Sciences, 07/2023.
- Seminar Talk, MPIM, Bonn, 06/2023.
- Seminar Talk, Caltech, 05/2023.
- Conference Talk, MIT, 05/2023.
- Seminar Talk, Brown University, 05/2023.
- Conference Talk, University of Miami, 04/2023, Video.
- Seminar talk, Stony Brook, 10/2022.
- Seminar talk, Peking University, 04/2022.
- Seminar talk, Morningside Center of Mathematics Chinese Academy of Sciences, Beijing, 04/2022
- Seminar talk, University of Warsaw, 12/2021.
- Seminar talk, Gauge Theory Virtual, 11/2021, Video.
- Seminar talk, MIT, 11/2021.
- Seminar talk, Caltech, 10/2021.
- Seminar talk, Peking University, 10/2021.
- Seminar talk, Princeton, 09/2021.
- Summer School on 4-manifolds, Georgia Tech, 07/2021
- Group report, Summer Trisection Workshop, 06/2021.
- Conference talk, NCNGT, 06/2021, Part I, Part II.
- Seminar talk, Peking University, 06/2021.
- Seminar talk, Stanford, 03/2021, Video.
- Seminar talk, Peking University, 03/2021.
Updated in 11/2023