Fan Ye 叶 帆

Email: fy260 at cam.ac.uk

I am a PhD candidate in Maths at University of Cambridge. My supervisor is Jacob Rasmussen. I will be on the job market this fall. You can see my complete CV here.

I am interested in low-dimensional topology, especially about gauge theory (Instanton, monopole, Heegaard Floer homology) and knot polynomials (Khovanov homology, $\mathfrak{sl}_n$ homology, HOMFLY-PT polynomial). I also have interests in symplectic geometry and mathematical physics.

Research

[6] SU(2) representations and a large surgery formula
(Joint with Zhenkun Li) ArXiv:2107.11005 || PDF

[5] An enhanced Euler characteristic of sutured instanton homology
(Joint with Zhenkun Li) ArXiv:2107.10490 || PDF

[4] Instanton Floer homology, sutures, and Euler characteristics
(Joint with Zhenkun Li, submitted) ArXiv:2101.05169 || PDF

[3] Sutured instanton homology and Heegaard diagrams
(Joint with John A. Baldwin and Zhenkun Li, submitted) ArXiv:2011.09424 || PDF

[2] Instanton Floer homology, sutures, and Heegaard diagrams
(Joint with Zhenkun Li, submitted) ArXiv:2010.07836 || PDF

[1] Constrained knots in lens spaces
(Accepted by Algebraic & Geometric Topology) ArXiv:2007.04237 || PDF || List of constrained knots || Data || Talk || Slides || Poster

Selected Talks

  • A large surgery formula for instanton Floer homology, Princeton, Sept. 2021.
  • Knot Floer homology and trisections (group report), Summer Trisection Workshop, June 2021.
  • Dimension bounds on sutured instanton homology, NCNGT, June 2021, Part I, Part II.
  • Constrained knots in lens spaces, Stanford, Mar. 2021, Video

Awards and Honors

  • Smith-Rayleigh and Knight-Rayleigh Prize 2021, Group 2, 2021.
  • Outstanding Graduates in Peking University, 2019.
  • Bronze Medel in Alibaba Global Mathematics Competition, 2018.
  • May Fourth Scholarship, 2017.
  • Winning Prize in S.T. Yau College Student Mathematics Contests, 2017.
  • Honorable Mention in Mathematical Contest In Modeling (MCM), 2017.
  • Accessit in China Undergraduate Mathematical Contest in Modeling, 2016.
  • Merit Student in Peking University, 2016.

Services

  • The chief editor for publications at School of Mathematical Sciences, Peking University, 2016-2018.
  • The resposible editor for PKU YOUTH, a popular publication at Peking University, 2016-2017.
  • The vice minister for the development department of the student union at School of Mathematical Sciences, Peking University, 2015-2016.

Updated in Sept. 2021