Gary Fishman

I am a fifth-year Ph.D. student at National Taiwan University, advised by Chee-Chun Leung (梁次震). Before coming to NTU I studied math at the University of Washington.

I study equations of the form $\int_0^\infty e^{-2\pi x^2} \, dx$. I am also interested in the groups \(H_k(\mathcal M_g, \mathbb Q)\) and $\pi_k(\mathrm{Sym}^\infty \mathcal M^\mathrm{trop}_g)$.

Here is my CV.

Contact

email: fishman (at) university . edu
office: Cosmology Hall R402
address: No. 1, Sec. 4, Roosevelt Rd.
Taipei City 106, Taiwan (R.O.C.)

Research Interests

Publications

  1. "Descartes' rule of signs for finite fields," in preparation.
  2. "Vector encoding of phylogenetic trees by ordered leaf attachment," coauthored with Erick Matsen and Cheng Zhang, submitted.
    [arxiv]
  3. "Lower rational approximations and Farey staircases," Integers 24 (2024), paper A37.
    [arXiv] [DOI] [pdf] [bibtex]
  4. "The floor quotient partial order," coauthored with Jeffrey Lagarias, Advances in Applied Mathematics 153 (2024).
    [arXiv] [DOI] [bibtex]
  5. "Derangements and the p-adic incomplete gamma function," coauthored with Andrew O'Desky, Transactions of the American Mathematical Society 376 (2023), pp. 1065-1087.
    [arXiv] [DOI] [bibtex]

Notes and Presentations

Teaching

I have experience teaching the fundamental theorem of calculus \[ \int_a^b f'(x) \, dx = f(b) - f(a) .\] This is related to the isomorphism $$\mathrm{Pic}^0(X) \cong H^0(X, \Omega^1)^\vee / H_1(X, \mathbb Z)$$ when $X$ is an algebraic curve.

University of Washington

Service

Organizer Journal Reviewer

Misc. Links