# Fan Ye 叶 帆 (Yè 4 Fān 1) ![Fan2023](/sites/g/files/omnuum10216/files/fanye/files/fan1.jpg) New email: flyye at math dot pku dot edu dot cn Old email: fanye at math dot harvard dot edu, which will be inactive soon. **\*\*This is my old homepage. I'll update a new homepage** [**floer.wiki**](https://floer.wiki) **soon and it will contain more information. Please check again in the future.** I moved to Peking University as an assistant professor. Previously, I’m a [Benjamin Peirce Fellow](https://www.math.harvard.edu/peoples-categories/benjamin-peirce-fellows/) and a [Simons collaboration postdoc](https://sites.google.com/view/simons-newstructures/our-team/affiliated-postdocs?authuser=0) at [Harvard Math Department](https://www.math.harvard.edu/). My mentor is [Peter Kronheimer](https://people.math.harvard.edu/~kronheim/). I finished my Ph.D. program in [Maths](https://www.maths.cam.ac.uk/) at [University of Cambridge](https://www.cam.ac.uk/) and my supervisor is [Jacob Rasmussen](https://www.dpmms.cam.ac.uk/~jar60/). [Here](https://faniel.wiki/about/CV%20Fan%20Ye.pdf) 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](https://arxiv.org/abs/2512.24206) || [PDF](https://faniel.wiki/paper/INSTANTON%202-TORSION%20AND%20FIBERED%20KNOTS.pdf) || [Talk](https://www.youtube.com/watch?v=Z3ltYNI61a0&list=PLZut3oE4FI0xLgQWla2cdshSJUKtXDsAb&index=13) **\[14\] Singular instanton homology of dual knots** submitted, [arXiv:2511.19883](https://arxiv.org/abs/2511.19883) || [PDF](https://faniel.wiki/paper/Singular%20instanton%20homology%20of%20dual%20knots.pdf) **\[13\] Instanton dimensions of knot surgeries over arbitrary fields** Joint with Zhenkun Li, submitted, [arXiv:2511.17877](https://arxiv.org/abs/2511.17877) || [PDF](https://faniel.wiki/paper/Instanton%20dimensions%20of%20knot%20surgeries%20over%20arbitrary%20fields.pdf) **\[12\] Instanton 2-torsion and Dehn surgeries** Joint with Zhenkun Li, submitted, [arXiv:2508.03394](https://arxiv.org/abs/2508.03394) || [PDF](https://faniel.wiki/paper/Instanton%202-torsion%20and%20Dehn%20surgeries.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.2025.110289](https://doi.org/10.1016/j.aim.2025.110289)[arXiv:2405.16252](https://arxiv.org/abs/2405.16252) || [PDF](https://faniel.wiki/paper/2-torsion%20in%20instanton%20Floer%20homology.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](https://doi.org/10.1007/s00208-024-03074-6) || [arXiv:2209.11018](https://arxiv.org/abs/2209.11018) || [PDF](https://faniel.wiki/paper/KNOT%20SURGERY%20FORMULAE%20FOR%20INSTANTON%20FLOER%20HOMOLOGY%20II.pdf) **\[9\] The guts of nearly fibered knots** Joint with Zhenkun Li, accepted by **Algebr. Geom. Topol.**, [arXiv:2208.05382](https://arxiv.org/abs/2208.05382) || [PDF](https://faniel.wiki/paper/The%20guts%20of%20nearly%20fibered%20knots.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](https://doi.org/10.2140/gt.2024.28.1891) || [arXiv:2206.10077](https://arxiv.org/abs/2206.10077) || [PDF](https://faniel.wiki/paper/KNOT%20SURGERY%20FORMULAE%20FOR%20INSTANTON%20FLOER%20HOMOLOGY%20I.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](https://doi.org/10.2140/gt.2024.28.1891) || [arXiv:2110.02874](https://arxiv.org/abs/2110.02874) || [PDF](https://faniel.wiki/paper/Small%20Dehn%20surgery%20and%20SU2.pdf) **\[6\] SU(2) representations and a large surgery formula** Joint with Zhenkun Li, submitted, [arXiv:2107.11005](https://arxiv.org/abs/2107.11005) || [PDF](https://faniel.wiki/paper/SU2%20representations%20and%20a%20large%20surgery%20formula.pdf) || [Talk](https://gaugetheoryvirtual.wordpress.com/f-ye-11-18-2021/) || [Slides](https://faniel.wiki/paper/large_surgery_formula_slides.pdf) **\[5\] 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](https://doi.org/10.1093/imrn/rnad066) || [arXiv:2107.10490](https://arxiv.org/abs/2107.10490) || [PDF](https://faniel.wiki/paper/An%20enhanced%20Euler%20characteristic%20of%20sutured%20instanton%20homology.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](https://doi.org/10.4171/QT/182) || [arXiv:2101.05169](https://arxiv.org/abs/2101.05169) || [PDF](https://faniel.wiki/paper/Instanton%20Floer%20homology,%20sutures,%20and%20Euler%20characteristics.pdf) || Talk, [Part I](https://www.youtube.com/watch?v=LjV_XnsJI1M), [Part II](https://www.youtube.com/watch?v=pmu-XjX1hk0) || [Slides](https://faniel.wiki/paper/dim_SHI_slides.pdf) **\[3\] 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](https://doi.org/10.1112/S0010437X23007303) || [arXiv:2011.09424](https://arxiv.org/abs/2011.09424) || [PDF](https://faniel.wiki/paper/Sutured%20instanton%20homology%20and%20Heegaard%20diagrams.pdf) || [Talk by Zhenkun Li](https://www.youtube.com/watch?v=crd0T_8dNNM) **\[2\] Instanton Floer homology, sutures, and Heegaard diagrams** Joint with Zhenkun Li, **J. Topol.** 15(1): 39-107, 2022. [DOI:10.1112/topo.12218](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/topo.12218) || [arXiv:2010.07836](https://arxiv.org/abs/2010.07836) || [PDF](https://faniel.wiki/paper/Instanton%20Floer%20homology,%20sutures,%20and%20Heegaard%20diagrams.pdf) || [Talk by Zhenkun Li](https://gaugetheoryvirtual.wordpress.com/z-li-11-12-2020/) **\[1\] Constrained knots in lens spaces** **Algebr. Geom. Topol.** 23(3): 1097–1166, 2023. [DOI: 10.2140/agt.2023.23.1097](https://msp.org/agt/2023/23-3/p03.xhtml)|| [arXiv:2007.04237](https://arxiv.org/abs/2007.04237) || [PDF](https://faniel.wiki/paper/Constrained%20knots%20in%20lens%20spaces.pdf) || [List of constrained knots](https://faniel.wiki/paper/SnapPy%20manifolds%20and%20constrained%20knots.xlsx) || [Data](https://doi.org/10.7910/DVN/GLFLHI) || [Talk](https://stanford.zoom.us/rec/play/LLDXRIRKb9lFNXG3isy0M_DFZj-UQ85VdB7hljZt0zjr6PYD0PwbfLmoGbMt1En1cV8gQi3GbrSxhlNR.SydvLHIKp2lWyc_4?startTime=1617123667000&_x_zm_rtaid=J08C5BowROqDhmx7lsBWGw.1617459798855.0c3da602c3002147d7475804c41e2129&_x_zm_rhtaid=522) || [Slides](https://faniel.wiki/paper/constrained_knots_slides.pdf) || [Poster](https://faniel.wiki/paper/Constrained_knots_poster.pdf) **\[0\] 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](https://www.repository.cam.ac.uk/handle/1810/337688) || [PDF](https://faniel.wiki/paper/Thesis_Fan%20Ye%20final220531.pdf) ## Conferences and Talks - [Mini-course](https://www.math.pku.edu.cn/kxyj/xzky/171600.htm), Peking University, 12/2025. - [Seminar Talk](https://maths.whu.edu.cn/info/1115/136841.htm), Wuhan University, 05/2025. - [Seminar Talk](https://www.math.pku.edu.cn/kxyj/xsbg/tlb/topology/163564.htm), Peking University, 12/2024. - [Seminar Talk](https://www.caltech.edu/campus-life-events/calendar/geometry-and-topology-seminar-90296), California Institute of Technology (Caltech), 10/2024. - [Seminar Talk](https://mathematics.miami.edu/events/seminars/index.html), University of Miami, 04/2024. - [Seminar Talk](https://www.math.princeton.edu/events/towards-isomorphisms-among-floer-homologies-2024-04-18t203000), Princeton University, 04/2024. - [Seminar Talk](https://math.osu.edu/events/towards-isomorphisms-among-floer-homologies), Ohio State University (OSU), 02/2024. - [Seminar Talk](https://www-math.umd.edu/research/seminars/geometry-topology-seminar.html#view-abstract-16), University of Maryland (UMD), 02/2024. - [Seminar Talk](https://math.wustl.edu/events/geometry-and-topology-seminar-towards-isomorphisms-among-floer-homologies), Washington University in St. Louis (WUSTL), 01/2024. - [Seminar Talk](https://calendars.illinois.edu/detail/7421/33474495), University of Illinois Urbana-Champaign (UIUC), 10/2023. - Seminar Talk, Boston College, 09/2023. - [Seminar Talk](https://sites.google.com/view/gagemartin/harvard-gauge-theory-and-topology-seminar), Harvard University, 09/2023. - [Seminar Talk](http://www.amss.cas.cn/mzxsbg/202307/t20230713_6809485.html), 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](https://www.mpim-bonn.mpg.de/node/12243), Max Planck Institute for Mathematics (MPIM), Bonn, 06/2023. - [Seminar Talk](https://sites.google.com/site/caltechgtseminar/home), California Institute of Technology (Caltech), 05/2023. - [Conference Talk](https://sites.google.com/view/instantonsandfoams/schedule), Massachusetts Institute of Technology (MIT), 05/2023. - [Seminar Talk](https://www.math.brown.edu/reschwar/seminar.html), Brown University, 05/2023. - [Conference Talk](https://www.youtube.com/watch?v=Z3ltYNI61a0&feature=youtu.be), University of Miami, 04/2023, [Video](https://www.youtube.com/watch?v=Z3ltYNI61a0&list=PLZut3oE4FI0xLgQWla2cdshSJUKtXDsAb&index=13&t=1420s). - [Seminar talk](https://www.math.stonybrook.edu/~sunscorch/grownup_seminar.html), Stony Brook University, 10/2022. - [Seminar talk](https://www.math.pku.edu.cn/kxyj/xsbg/tlb/topology/137759.htm), Peking University, 04/2022. - [Seminar talk](http://www.amss.cas.cn/mzxsbg/202204/t20220412_6425367.html), Morningside Center of Mathematics Chinese Academy of Sciences, Beijing, 04/2022. - [Seminar talk](https://www.mimuw.edu.pl/~mcboro/knot.html), University of Warsaw, 12/2021. - [Seminar talk](https://gaugetheoryvirtual.wordpress.com/seminar-page/), Gauge Theory Virtual, 11/2021, [Video](https://gaugetheoryvirtual.wordpress.com/f-ye-11-18-2021/). - [Seminar talk](https://sites.google.com/view/anthony-conway/activities/mit-geometry-and-topology-seminar-fall-2021), Massachusetts Institute of Technology (MIT), 11/2021. - [Seminar talk](https://sites.google.com/site/caltechgtseminar/home), California Institute of Technology (Caltech), 10/2021. - [Mini-course](https://bicmr.pku.edu.cn/content/show/70-2573.html), Beijing International Center for Mathematical Research (BICMR), 10/2021 - [Seminar talk](https://www.math.pku.edu.cn/kxyj/xsbg/tlb/topology/131847.htm), Peking University, 10/2021. - [Seminar talk](https://www.math.princeton.edu/events/large-surgery-formula-instanton-floer-homology-2021-09-09t133000), Princeton University, 09/2021. - [Summer School on 4-manifolds](https://ttss.math.gatech.edu/), Georgia Tech, 07/2021. - Group report, [Summer Trisection Workshop](https://sites.google.com/view/stw2021), 06/2021. - Conference talk, [NCNGT](https://sites.google.com/view/ncngt2021/topic-groups/floer-khovanov), 06/2021, [Part I](https://www.youtube.com/watch?v=LjV_XnsJI1M), [Part II](https://www.youtube.com/watch?v=pmu-XjX1hk0). - [Seminar talk](https://www.math.pku.edu.cn/kxyj/xsbg/tlb/topology/128682.htm), Peking University, 06/2021. - [Seminar talk](https://mathematics.stanford.edu/events/topology/constrained-knots-lens-spaces), Stanford University, 03/2021, [Video](https://stanford.zoom.us/rec/play/LLDXRIRKb9lFNXG3isy0M_DFZj-UQ85VdB7hljZt0zjr6PYD0PwbfLmoGbMt1En1cV8gQi3GbrSxhlNR.SydvLHIKp2lWyc_4?startTime=1617123667000&_x_zm_rtaid=J08C5BowROqDhmx7lsBWGw.1617459798855.0c3da602c3002147d7475804c41e2129&_x_zm_rhtaid=522). - [Seminar talk](https://www.math.pku.edu.cn/kxyj/xsbg/tlb/topology/126236.htm), Peking University, 03/2021. **Updated in 01/2026**