Harry Richman

photo

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

I am currently a postdoc in the Matsen group, part of the Herbold Computational Biology Program at the Fred Hutch Cancer Center. I was previously a postdoc 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 2019.

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

Contact

Teaching

Research

1. "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.


2. "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.


3. "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.


4. "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.


5. "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.


6. "The tropical Manin-Mumford conjecture," International Mathematics Research Notices 2023.21 (2023), pp. 18714-18751.
   arXiv:2112.00168. DOI: 10.1093/imrn/rnad098.


7. "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.

Preprints

8. "The distribution of Weierstrass points on a tropical curve," submitted.
   arXiv:1809.07920.


9. "Tropical Weierstrass points and Weierstrass weights," coauthored with Omid Amini and Lucas Gierczak, submitted.
   arXiv:2303.07729


10. "The family of $a$-floor quotient partial orders," coauthored with Jeffrey Lagarias, submitted.


11. "Lower rational approximations and Farey staircases."
    arXiv:2303.02935.


12. "Counting two-forests and random cut size via potential theory," coauthored with Farbod Shokrieh and Chenxi Wu.
    arXiv:2308.03859


13. "Minors of tree distance matrices," coauthored with Farbod Shokrieh and Chenxi Wu, in preparation.


14. "Origami hexagon deformations and the flip graph," coauthored with Y. Liu, in preparation.


15. "The Möbius function of the poset of triangular numbers under divisibility," coauthored with R. Pandey, in preparation.

Ph.D. thesis

16. "Weierstrass points and torsion points on tropical curves."
    published version: link (local)

Notes and Presentations

• "Matchings in convergent graph sequences," March 2017 notes


• "Moduli space of tropical curves," June 2017 notes


• "Local Gauss-Lucas theorem," July 2017 slides


• "Dilated floor functions having nonnegative commutator," July 2017 poster slides AMS


• "Descartes' rule and beyond," September 2017 slides


• "Distribution of tropical Weierstrass points," September 2018 slides poster animation


• "The poset of floor quotients," December 2019 slides


• "Weierstrass points and torsion points on tropical curves," March 2020 slides


• "Continuity over p-adic numbers," November 2021 slides


• "Derangements and a p-adic incomplete gamma function," November 2021 slides


• "Uniform bounds on tropical torsion points," January 2022 slides poster


• "Distance matrices and equilibirum measures on trees," December 2022 slides


• "Tropical weights of Weierstrass points," April 2023 poster


• "Phylogenetic trees to integer vectors," July 2023 slides

Links