I am interested in problems in tropical geometry (what's that??), phylogenetics, combinatorics, and number theory.

I am currently a postdoc at NCTS mentored by Liang-Chung Hsia. I previously held postdoc positions in the Matsen group, part of the Herbold Computational Biology Program at the Fred Hutch Cancer Center, and at the University of Washington where my mentor was Farbod Shokrieh. Before that I was a graduate student at the University of Michigan where my advisors were David Speyer and Jeff Lagarias. I was on the academic job market in fall 2023.

Before graduate school I studied math at MIT and the Math in Moscow program.

Contact

email:	hrichman (аt) ncts (dot) ntu (dot) edu (dot) tw
	hrichman (аt) alum (dot) mit (dot) edu
office:	Room 402, Cosmology Building
address:	台北市 羅斯福路 4段 1號
	台灣大學 次震宇宙館 503室
	Room 503, Cosmology Building
	National Taiwan University
	No. 1, Sec. 4, Roosevelt Rd.
	Taipei City 106, Taiwan (R.O.C.)
github:	harryrichman

Teaching

Mentored research projects

• WXML Counting spanning trees, Autumn 2021 - Winter 2022
• MREG Rational Catalan combinatorics, Summer 2021
• LOG(M) Origami on Lattices, Winter 2019

Research

My work can be found on arXiv, Google Scholar, MathSciNet, ORCID, and zbMATH.

Preprints

• "Vector encoding of phylogenetic trees by ordered leaf attachment," coauthored with Erick Matsen and Cheng Zhang.
  arxiv:2503.10169
• "Principal minors of tree distance matrices," coauthored with Farbod Shokrieh and Chenxi Wu, submitted.
  arXiv:2411.11488 (local link)
• "A Ricci flow on graphs from effective resistance," coauthored with A. Dawkins, V. Gupta, M. Kempton, W. Linz, J. Quail, and Z. Stier, submitted.
  arXiv:2403.01151
• "Node resistance curvature in Cartesian graph products," coauthored with A. Dawkins, V. Gupta, M. Kempton, W. Linz, J. Quail, and Z. Stier, submitted.
  arXiv:2403.01037
• "The Möbius function of the poset of triangular numbers under divisibility," coauthored with Rohan Pandey, submitted.
  arXiv:2402.07934
• "Counting two-forests and random cut size via potential theory," coauthored with Farbod Shokrieh and Chenxi Wu, submitted.
  arXiv:2308.03859
• "Tropical Weierstrass points and Weierstrass weights," coauthored with Omid Amini and Lucas Gierczak, submitted.
  arXiv:2303.07729

Published

1. "The family of a-floor quotient partial orders," coauthored with Jeffrey Lagarias, in Proceedings of Combinatorial and Additive Number Theory VI (2025), pp. 283-318.
   arXiv:2403.04342. DOI:10.1007/978-3-031-65064-2_15
2. "Lower rational approximations and Farey staircases," Integers 24 (2024), paper A37.
   arXiv:2303.02935. DOI:10.5281/zenodo.10944039. journal version:link.
3. "The distribution of Weierstrass points on a tropical curve," Selecta Mathematica 30 (2024).
   arXiv:1809.07920. DOI:10.1007/s00029-024-00919-5.
4. "The floor quotient partial order," coauthored with Jeffrey Lagarias, Advances in Applied Mathematics 153 (2024).
   arXiv:2212.11689. DOI:10.1016/j.aam.2023.102615.
5. "The tropical Manin-Mumford conjecture," International Mathematics Research Notices 2023.21 (2023), pp. 18714-18751.
   arXiv:2112.00168. DOI:10.1093/imrn/rnad098.
6. "Counting tripods on the torus," coauthored with Jayadev S. Athreya and David Aulicino, Arnold Mathematical Journal 9 (2023), pp. 359-379.
   arXiv:2111.01891. DOI:10.1007/s40598-022-00216-z.
7. "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:2012.04615. DOI:10.1090/tran/8716.
8. "Dilated floor functions having nonnegative commutator II. Negative dilations," coauthored with Jeffrey Lagarias, Acta Arithmetica 196.2 (2020), pp. 163-186.
   arXiv:1907.09641. DOI:10.4064/aa190628-14-1.
9. "Dilated floor functions having nonnegative commutator I. Positive and mixed sign dilations," coauthored with Jeffrey Lagarias, Acta Arithmetica 187.3 (2019), pp. 271-299.
   arXiv:1806.00579. DOI:10.4064/aa180602-21-9.
10. "Dilated floor functions that commute," coauthored with J. C. Lagarias and T. Murayama, American Math. Monthly 123.10 (2016), pp. 1033-1038.
    arXiv:1611.05513. DOI:10.4169/amer.math.monthly.123.10.1033.

Ph.D. thesis

0. "Weierstrass points and torsion points on tropical curves."
   official version: link (local link)

Conference Proceedings

• FPSAC 2025, "Principal minors of tree distance matrices."
• ICLR 2025, with Tianyu Xie, Jiansi Gao, Frederick A. Matsen IV, Cheng Zhang, "PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders."
  arxiv:2502.04730
• FPSAC 2022, with Andrew O'Desky, "Derangements and the p-Adic Incomplete Gamma Function."
  online:link
• FPSAC 2019, "The distribution of Weierstrass points on a tropical curve."
  online:link

Notes and Presentations

• "Ricci flow on graphs from effective resistance," January 2024 slides
• "Phylogenetic trees to integer vectors," July 2023 slides tldr slides poster
• "Tropical weights of Weierstrass points," April 2023 poster slides
• "Distance matrices and equilibirum measures on trees," December 2022 slides
• "Uniform bounds on tropical torsion points," January 2022 slides poster
• "Continuity over p-adic numbers," November 2021 slides
• "Derangements and a p-adic incomplete gamma function," November 2021 slides poster
• "Weierstrass points and torsion points on tropical curves," March 2020 slides
• "The poset of floor quotients," December 2019 slides
• "Distribution of tropical Weierstrass points," September 2018 slides poster animation
• "Descartes' rule and beyond," September 2017 slides
• "Dilated floor functions having nonnegative commutator," July 2017 poster slides AMS
• "Local Gauss-Lucas theorem," July 2017 slides
• "Moduli space of tropical curves," June 2017 notes
• "Matchings in convergent graph sequences," March 2017 notes

Interactive content

• Ricci-Foster curvature on graphs link
• Partial order of floor quotients link
• Weierstrass points on graphs link
• Partial order of triangular number divisibility link

Links

Math-related

Analysis quals

Math Subject Classification browse and search, resource from zbMATH

MR Lookup find math references in bibtex format, resource from AMS

OEIS Online Encyclopedia of Integer Sequences

FindStat database and search engine for combinatorial statistics and maps

COS++ The Combinatorial Object Server, generate combinatorial objects

M_{g,n}-bar about the moduli space of stable nodal curves of genus g with n marked points

Non-math

Rubik's cube

Origami simulator built by Amanda Ghassaei

Windy wind map

Semi-math

Quotes about math

Multiline formulas guidelines provided by Acta Arithmetica

Eugenia Cheng on the lecture system

Why should I do math? Reasons by Tao Lin (43., 35., 31., 10., 28., 8., 11., 14., 41., 26., 21., 18.)