Google Scholar  UTD Faculty Profile  ORCID 
Google Scholar  UTD Faculty Profile  ORCID 
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 Ktheoretic jeudetaquin 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. Stembridgeas 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 132page monograph that extends N. Reading's Coxetersortable elements and the cluster complex to the positive braid monoidextending D. Armstrong's Fussification of noncrossing partitions (after P. Edelman) to the other CoxeterCatalan families. 

Rational Noncrossing Catalan Combinatorics (with P. Galashin, T. Lam, and M.T. Trinh) is a 42page 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 PopTsack Torsing (with C. Defant) studies the Bessis dual version of C. Defant's Coxeter PopStack Sorting mapthat 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 popstack sorting and type A crystal lattices and The Ungar games (with N. Kravitz). 
Google Scholar  UTD Faculty Profile  ORCID 
Recording  Event/Slides  Year 

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 

Strange Checkspectations 
FPSAC 
2021 
Independence Posets 
FPSAC 
2020 
Google Scholar  UTD Faculty Profile  ORCID 
Course Name  Notes 

MATH 6311: Algebra I (graduate course) 

MATH 3315: Discrete Math and Combinatorics  
Honors Reading Topics in Algebraic 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  
MATH 6311: Algebra I (graduate course) 
S18, S19, S20, S21, F21, F22  
Honors Reading Topics in Algebraic Combinatorics 
F19, F20, F21, F22 
Name  Degree  Project  Year 

Weston Miller  Honors Bachelor's Thesis  Rational Catalan Numbers for Complex Reflection Groups Project code available here 
2023 
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  ELshellability 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 
Organization  Title 

Annals of Combinatorics  Associate Editor 
Formal Power Series and Algebraic Combinatorics  Funding Coordinator 
Cochair of the website and computer committee (with John Zweck)
Member of the outreach committee: Member of the K12 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 
Google Scholar  UTD Faculty Profile  ORCID 
Title (click for proposal)  Funding agency  Year 

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+ 
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 