Fan's homepage

Fan Ye 叶 帆 (Yè4 Fān1)

Email: fanye at math dot harvard dot edu

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.

Research

[1] 2-torsion in instanton Floer homology
Joint with Zhenkun Li, submitted, arXiv:2405.16252 || PDF

[2] Knot surgery formulae for instanton Floer homology II: applications
Joint with Zhenkun Li, accepted by Math. Ann. , arXiv:2209.11018 || PDF

[3] The guts of nearly fibered knots
Joint with Zhenkun Li, submitted, arXiv:2208.05382 || PDF

[4] Knot surgery formulae for instanton Floer homology I: the main theorem
Joint with Zhenkun Li, accepted by Geom. Topol. , arXiv:2206.10077 || PDF

[5] 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

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

[8] 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

[9] 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

[10] 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

[11] 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

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, 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.
• 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 08/2024