Google Scholar | UTD Faculty Profile | ORCID | arXiv |
Google Scholar | UTD Faculty Profile | ORCID | arXiv |
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). | |
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Cataland: Why the Fuss? (with C. Stump and H. Thomas) was 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. |
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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). |
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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). |
Charmed Roots and the Kroweras Complement (with B. DequĂȘne, G. Frieden, A. Iraci, F. Schreier-Aigner, and Hugh Thomas) continues the saga of trying to find a bijection between nonnesting partitions and noncrossing partitions. The title is an unfortunate portmanteau of Germain Kreweras's last name and rowmotion. As I said at FPSAC: "I was hired for this project as the marketing consultant. They told me to write the introduction to the paper. At some point, about halfway through writing this introduction, I decided I should check out what the paper was all about. And that's what I'm here to tell you about today." |
Google Scholar | UTD Faculty Profile | ORCID | arXiv |
Recording | Event/Slides | Year |
---|---|---|
Catalan Recollections Lecture 1 Lecture 2 ![]() |
SLC93 ![]() |
2025 |
Charmed Roots and the Kroweras Complement![]() |
FPSAC 2024 ![]() |
2024 |
Coxeter Combinatorics and Braid Varieties![]() |
ICMS ![]() |
2023 |
Rational Noncrossing Catalan Combinatorics![]() |
OPAC ![]() |
2022 |
Semidistrim Lattices ![]() |
BIRS ![]() |
2021 |
Strange Expectations ![]() |
UCLA Combinatorics Seminar ![]() |
2020 |
Independence Posets ![]() |
Triangle Lectures in Combinatorics ![]() |
2020 |
Poster | Event | Year |
---|---|---|
Pop, Crackle, Snap (and Pow): Some Facets of Shards ![]() |
FPSAC 2023 ![]() |
2021 |
Strange Checkspectations ![]() |
FPSAC 2021 ![]() |
2021 |
Independence Posets ![]() |
FPSAC ![]() |
2020 |
Google Scholar | UTD Faculty Profile | ORCID | arXiv |
Course Name | Notes |
---|---|
MATH 3315: Discrete Math and Combinatorics | ![]() |
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, F23, S24, F24 |
MATH 6311: Algebra I (graduate course) |
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S18, S19, S20, S21, F21, F22, F23 |
MATH 6312: Combinatorics and Graph Theory (graduate course) |
![]() | F24 |
Honors Reading Topics in Algebraic Combinatorics |
F19, F20, F21, F22, F23, F24 | MATH 2419: Calculus II (honors section) |
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S24 |
Name | Degree | Project | Year |
---|---|---|---|
Weston Miller | Honors Bachelor's Thesis | Rational Catalan Numbers for Complex Reflection Groups Project code available here |
2024 |
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 |
2022 |
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 |
2022 |
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 |
2020 |
Benjamin Cotton | Honors Bachelor's Thesis | A core model for G2 Published in Involve |
2020 |
Google Scholar | UTD Faculty Profile | ORCID | arXiv |
Organization | Title |
---|---|
Annals of Combinatorics![]() | Associate Editor |
Chair of the website and computer committee
Member of the outreach committee: ![]() Member of the K-12 mathematics competitions committee Faculty organizer for the Putnam Club and William Lowell Putnam Mathematical Exam |
Link | Subject | News Stations |
---|---|---|
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2022 Mega Millions lottery jackpot | CBS 11 (also NBC 5) |
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2018 NCAA men's basketball bracket | WFAA and on over 15 television stations nationwide |
Google Scholar | UTD Faculty Profile | ORCID | arXiv |
Title (click for proposal) | Funding agency | Year |
---|
Title (click for proposal) | Funding agency | Reviews | Year |
---|---|---|---|
New Techniques in Algebraic Combinatorics | Simons | (Not provided) | 2018 |
Combinatorics and Braid Varieties | NSF | Reviews Panel Summary Officer Summary | 2023+ |
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 |