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About Me

I received my Ph.D. in 2013 from the University of Minnesota, under the supervision of Dennis Stanton; the title of my dissertation was "Cataland". I then had the opportunity to spend 2+1 wonderful years at LaCIM as a postdoc—my original offer was for two years, but I was able to stay for one additional year because Hugh Thomas came to LaCIM with a Canada Research Chair and generously extended my postdoc. (Thanks to this extra year, Hugh and I were able to invert the sweep map!)

After one year at the University of California, Santa Barbara as Jon McCammond's postdoc, I started at my current tenure-track position at the University of Texas at Dallas in 2017.

I am roughly Γ() years old.

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Selected Papers

My research is in algebraic combinatorics, centered around reflection, braid, and Lie groups. I have been very fortunate to have had many brilliant collaborators, with whom I have written some very nice papers. Here are a few of my favorites:

Promotion and Rowmotion (with J. Striker) unifies various results in what J. Propp calls "Dynamical Algebraic Combinatorics". Later related work includes Rowmotion in Slow Motion and Independence Posets (with H. Thomas), and Semidistrim Lattices (with C. Defant).
Doppelgängers (with Z. Hamaker, R. Patrias, and O. Pechenik) uses K-theoretic jeu-de-taquin to give an explicit bijection between plane partitions in a rectangle and plane partitions in a trapezoid. This solves an old problem considered by both R. Proctor and J. Stembridge--as R. Proctor wrote "the question of a combinatorial correspondence...seems to be a complete mystery."
Sweeping up Zeta (with H. Thomas) inverts D. Armstrong, N. Loehr, and G. Warrington's sweep map, with applications to (q,t)-combinatorics. Inverting sweep is unexpectedly equivalent to a different problem that Hugh and I solved in 2012. Later related work includes Fixed Points of Parking Functions (with J. McCammond and H. Thomas).
Cataland: Why the Fuss? (with C. Stump and H. Thomas) is a 132-page monograph that extends N. Reading's Coxeter-sortable elements and the cluster complex to the positive braid monoid---extending D. Armstrong's Fussification of noncrossing partitions (after P. Edelman) to the other Coxeter-Catalan families.

Rational Noncrossing Catalan Combinatorics (with P. Galashin, T. Lam, and M.-T. Trinh) is a 42-page preprint that uses braid varieties to give the first uniform construction of rational noncrossing Catalan objects and the first uniform enumeration of noncrossing objects. These were both longstanding open problems, considered in both Why the Fuss? and Rational associahedra and noncrossing partitions (with D. Armstrong and B. Rhoades).
Coxeter Pop-Tsack Torsing (with C. Defant) studies the Bessis dual version of C. Defant's Coxeter Pop-Stack Sorting map--that is, we modify the definitions by replacing all instances of S (the simple reflections) with T (the set of all reflections). Later related work with C. Defant includes Crystal pop-stack sorting and type A crystal lattices and The Ungar games (with N. Kravitz).

Papers and Preprints

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Selected Talks

Recording Event/Slides Year
Rational Noncrossing Catalan Combinatorics
Semidistrim Lattices
Strange Expectations
UCLA Combinatorics Seminar
Independence Posets
Triangle Lectures in Combinatorics

Selected Posters

Poster Event Year
Strange Checkspectations
Independence Posets

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Since Fall 2017, I have taught 23 courses over 12 semesters at UTD— In 2020, I won UTD's School of Natural Science and Mathematics tenure-track teaching award. I completed the ACUE course in "Effective College Instruction" in Spring 2021.

I have advised four independent study courses, two senior capstone projects, and five honors senior theses (two of which resulted in publications). In 2022, I successfully graduated my first Ph.D. student, who is now tenure-track at a small liberal arts college.


Current Courses

Course Name Notes
MATH 6311: Algebra I
(graduate course)
MATH 3315: Discrete Math and Combinatorics
Honors Reading
Topics in Algebraic Combinatorics

Past Courses

Course Name Notes Semesters (click for reviews)
MATH 2417: Calculus I F17, F18a, F18b, F20
MATH 2419: Calculus II S22, S23
MATH 3315: Discrete Math and Combinatorics S19, F19, S20, F20, S21, F21, S22, F22, S23
MATH 6311: Algebra I
(graduate course)
S18, S19, S20, S21, F21, F22
Honors Reading
Topics in Algebraic Combinatorics
F19, F20, F21, F22

Selected Student Supervision

Name Degree Project Year
Weston Miller Honors Bachelor's Thesis Rational Catalan Numbers for Complex Reflection Groups
Project code available here
Priyojit Palit Ph.D. Dual Braid Presentations and Cluster Algebras
Won ``Best Graduate Blitz'' for his video presentation at the DFW Area 2021 Virtual Poster Competition in Mathematics
Yusuf Ahsanullah Honors Bachelor's Thesis Quantum Groups and Cluster Fans 2022
Deep Desai, Ramesh Kanakala, Ryan Lofton, Savitha Venkatesh, Ariba Tahsin Bachelor in Data Science - Capstone Project Software implementation of independence posets
Capstone Project Presentation Award: Honorable Mention - Creativity
Michelle Sferrazza Honors Capstone Project EL-shellability of noncrossing partition lattices 2022
Joshua Marsh Honors Bachelor's Thesis Nesting Nonpartitions
Published in Journal of Integer Sequences
Benjamin Cotton Honors Bachelor's Thesis A core model for G2
Published in Involve

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Algebraic Combinatorics

Organization Title
Annals of Combinatorics Associate Editor
Formal Power Series and Algebraic Combinatorics Funding Coordinator

UTD Department of Mathematical Sciences

Co-chair of the website and computer committee (with John Zweck)

Member of the outreach committee:
  • Yearly Weeks of Welcome recreational math activity table (with Maxim Arnold and Vladimir Dragovic)
  • $\pi$-day Buffon's noodle presentation (with Maxim Arnold)

  • Member of the K-12 mathematics competitions committee

  • Faculty organizer for the Putnam Club and William Lowell Putnam Mathematical Exam


    Link Subject News Stations
    2022 Mega Millions lottery jackpot CBS 11 (also NBC 5)
    2018 NCAA men's basketball bracket WFAA and on over 15 television stations nationwide

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    Grants under Review

    Title (click for proposal) Funding agency Year

    Grants Funded

    Title (click for proposal) Funding agency Reviews Year
    New Techniques in Algebraic Combinatorics Simons 2018
    Combinatorics and Braid Varieties NSF Reviews Panel Summary Officer Summary 2023+

    Grants Declined

    Title (click for proposal) Funding agency Reviews Year
    Independence Posets and Dynamical Algebraic Combinatorics NSF Reviews Panel Summary Officer Summary F21
    CAREER: Dynamical Algebraic Combinatorics NSF Reviews Panel Summary Officer Summary S21
    Independence Posets NSF Reviews Panel Summary Officer Summary F20
    Combinatorial Tools in Representation Theory NSF Reviews Panel Summary Officer Summary F19
    Geometry of Braid Groups in Combinatorics NSF Reviews Panel Summary Officer Summary F18
    New bijective techniques in algebraic combinatorics NSF Reviews Panel Summary Officer Summary F17