Fan's homepage

Fan Ye 叶 帆 (Yè4 Fān1)

Email: flyye at math dot pku dot edu dot cn

I moved to Peking University as an assistant professor. Previously, I’m a Benjamin Peirce Fellow and a Simons collaboration postdoc 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 knot theory, gauge theory, and Floer homology. Related topics: Heegaard Floer, Seiberg-Witten Floer, instanton Floer, symplectic Floer, embedded contact, Khovanov, Khovanov-Rozansky homology theories, contact topology, quantum topology, geometric analysis, mathematical physics.

Research

[15] Instanton 2-torsion and fibered knots
Joint with Deeparaj Bhat and Zhenkun Li, submitted, arXiv:2512.24206 || PDF

[14] Singular instanton homology of dual knots
submitted, arXiv:2511.19883 || PDF

[13] Instanton dimensions of knot surgeries over arbitrary fields
Joint with Zhenkun Li, submitted, arXiv:2511.17877 || PDF

[12] Instanton 2-torsion and Dehn surgeries
Joint with Zhenkun Li, submitted, arXiv:2508.03394 || PDF

[11] 2-torsion in instanton Floer homology
Joint with Zhenkun Li, Adv. Math., 472:Paper No. 110289, 55, 2025. DOI:10.1016/j.aim.2025.110289arXiv:2405.16252 || PDF

[10] Knot surgery formulae for instanton Floer homology II: applications
Joint with Zhenkun Li, Math. Ann., 391:6291–6371, 2025. DOI: 10.1007/s00208-024-03074-6 || arXiv:2209.11018 || PDF

[9] The guts of nearly fibered knots
Joint with Zhenkun Li, accepted by Algebr. Geom. Topol., arXiv:2208.05382 || PDF

[8] Knot surgery formulae for instanton Floer homology I: the main theorem
Joint with Zhenkun Li, Geom. Topol. 29(5): 2269—2342, 2025. DOI:10.2140/gt.2025.29.2269 || arXiv:2206.10077 || PDF

[7] Small Dehn surgery and SU(2)
Joint with John A. Baldwin, Zhenkun Li, and Steven Sivek, Geom. Topol. 28(4): 1891–1922, 2024. DOI: 10.2140/gt.2024.28.1891 || arXiv:2110.02874 || PDF

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

[5] An enhanced Euler characteristic of sutured instanton homology
Joint with Zhenkun Li, Int. Math. Res. Not. 2024(4): 2873-2936, 2024. DOI:10.1093/imrn/rnad066 || arXiv:2107.10490 || PDF

[4] 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

[3] 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

[2] 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

[1] Constrained knots in lens spaces
Algebr. 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

[0] 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

• Mini-ourse, Peking University, 12/2025.
• Seminar Talk, Wuhan University, 05/2025.
• Seminar Talk, Peking University, 12/2024.
• Seminar Talk, California Institute of Technology (Caltech), 10/2024.
• Seminar Talk, University of Miami, 04/2024.
• Seminar Talk, Princeton University, 04/2024.
• Seminar Talk, Ohio State University (OSU), 02/2024.
• Seminar Talk, University of Maryland (UMD), 02/2024.
• Seminar Talk, Washington University in St. Louis (WUSTL), 01/2024.
• Seminar Talk, University of Illinois Urbana-Champaign (UIUC), 10/2023.
• Seminar Talk, Boston College, 09/2023.
• Seminar Talk, Harvard University, 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, Max Planck Institute for Mathematics (MPIM), Bonn, 06/2023.
• Seminar Talk, California Institute of Technology (Caltech), 05/2023.
• Conference Talk, Massachusetts Institute of Technology (MIT), 05/2023.
• Seminar Talk, Brown University, 05/2023.
• Conference Talk, University of Miami, 04/2023, Video.
• Seminar talk, Stony Brook University, 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, Massachusetts Institute of Technology (MIT), 11/2021.
• Seminar talk, California Institute of Technology (Caltech), 10/2021.
• Mini-course, Beijing International Center for Mathematical Research (BICMR), 10/2021
• Seminar talk, Peking University, 10/2021.
• Seminar talk, Princeton University, 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 University, 03/2021, Video.
• Seminar talk, Peking University, 03/2021.

Updated in 12/2025