Research

I'm interested in the intersections between combinatorics and algebra. Some projects have focused on symmetric functions, Macdonald polynomials, representations of the symmetric group, parking functions, hyperplane arrangements, matroids, Schubert calculus, permutation statistics, rook theory, knot theory, pattern enumeration, and the descent algebra, although I'm always happy to add a new topic to the list. I've provided links below to many of my articles and talks. Feel free to contact me if you would like to see slides from a talk that are not posted here.

Here is my CV.

Preprints

• Tutte polynomials in superspace, with Brendon Rhoades and Vasu Tewari.

  • Submitted.

• The Hilbert series of the superspace coinvariant ring, with Brendon Rhoades.

  • Submitted.

Publications

• A symmetric function lift of torus link homology.

  • Combinatorial Theory, 3(3), dx.doi.org/10.5070/C63362795, 2023.

  • Extended abstract appeared in Proceedings of FPSAC 2022 as "The elliptic Hall algebra element Q_{m,n}^{k} (1)."

• Set superpartitions and superspace duality modules, with Brendon Rhoades.

  • Forum of Mathematics, Sigma, 10, E105, 2022.

• Chromatic nonsymmetric polynomials of Dyck graphs are slide positive, with Vasu Tewari and Philip B. Zhang.

  • Proceedings of the AMS, 150(5):1873-1888, 2022.

• Macdonald polynomials and chromatic quasisymmetric functions, with Jim Haglund. 

  • Electronic Journal of Combinatorics, 27(3):#P3.37, 2020.

• Vandermondes in superspace, with Brendon Rhoades. 

  • Transactions of the AMS, 373:4483-4516, 2020.

  • Extended abstract appeared in Proceedings of FPSAC 2020.

• The valley version of the Extended Delta Conjecture, with Dun Qiu.

  • Journal of Combinatorial Theory, Series A, 175:105271, 2020.

• Line configurations and r-Stirling permutations, with Brendon Rhoades. 

  • Journal of Combinatorics, Special Issue in Memory of Jeff Remmel, 10(3):411-431, 2019. 

• The Delta Conjecture, with Jim Haglund and Jeff Remmel. 

  • Transactions of the AMS, 370:4029-4057, 2018.

  • Extended abstract appeared in Proceedings of FPSAC 2016.

• Torus link homology and the nabla operator. 

  • Journal of Combinatorial Theory, Series A, 154:129-144, 2018.

  • Extended abstract accepted to Proceedings of FPSAC 2017.

• Tail positive words and generalized coinvariant algebras, with Brendon Rhoades. 

  • Electronic Journal of Combinatorics, 24(3):#P3.21, 2017.

• A weighted sum over generalized Tesler matrices. 

  • Journal of Algebraic Combinatorics, 45(3):825-855, 2017.

  • Extended abstract appeared in Proceedings of FPSAC 2015.

• An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions.

  • Electronic Journal of Combinatorics, 23(1):#P1.5, 2016.

  • Extended abstract appeared in Proceedings of FPSAC 2014.

• An extension of MacMahon's Equidistribution Theorem to ordered set partitions, with Jeff Remmel.

  • Journal of Combinatorial Theory, Series A, 34:242-277, 2015.

• Block patterns in Stirling permutations, with Jeff Remmel.

  • Journal of Combinatorics, 6:179-204, 2015.

• Bijections for the Shi and Ish arrangements, with Emily Sergel and Brendon Rhoades.

  • European Journal of Combinatorics, 39:1-23, 2014.

Dissertation

• Generalized Shuffle Conjectures for the Garsia-Haiman Delta Operator, UCSD, June 2015.

Talks

• "From polynomials to superspace," AMS Sectional Meeting, Tallahassee, March 2024.

• "Problems in superspace," Fields Institute Algebraic Combinatorics Seminar, March 2024.

• "Coinvariants in superspace," Waterloo Algebraic Combinatorics Seminar, January 2023.

• "Coinvariants in superspace," Georgia Tech Algebra Seminar, November 2022.

• "Coinvariants in superspace," University of Florida Combinatorics Seminar, October 2022.

• "The combinatorics, algebra, and geometry of torus links," CAGE Seminar, Philadelphia, May 2022.

• "A talk approximately about pi," Pi Day, Kennesaw State, March 2022.

• "Combinatorics of (n, n) torus link homology," AIM Research Group on Link Homology, August 2021.

• "Partitions inside a rectangle," University of Florida Combinatorics Seminar, January 2021.

• "The mathematics of voting districts," Kennesaw State Faculty Research Spotlight, September 2020.

  • Slides

• "The combinatorics of harmonic polynomials," Kennesaw State Discrete Math Seminar, September 2020.

  • Notes

• "Vandermondes in superspace," FPSAC Online, July 2020.

  • Video, slides

• "q-analogs of factorials and Fubini numbers," Portland State University Combinatorics & Number Theory Seminar, January 2020.

• "Toward set-valued LLT polynomials," Garsiafest, San Diego, June 2019.

  • Slides, abstract

• "Graph coloring and symmetric functions," Portland State University Combinatorics & Number Theory Seminar, November 2018.

• "Macdonald polynomials and chromatic functions," Workshop on Hessenberg Varieties in Combinatorics, Geometry, and Representation Theory, Banff, October 2018.

  • Slides

• "The combinatorics of symmetric quotient rings," UQAM Combinatorics Seminar, May 2018.

  • Slides, handout

• "S_n modules and Macdonald eigenoperators," AMS Sectional Meeting, Boston, April 2018.

  • Slides, handout

• "Lattice paths inside shapes," Haverford College, April 2018.

• "Lattice paths inside shapes," Lehigh Math Colloquium, April 2018.

  • Slides

• "Macdonald polynomials and chromatic functions," AMS Sectional Meeting, Nashville, April 2018.

• "The combinatorics of symmetric quotient rings," CAGE Seminar, Philadelphia, January 2018.

• "The combinatorics of symmetric quotient rings," University of Washington Combinatorics Seminar, November 2017.

• "The combinatorics of symmetric quotient rings," US Naval Academy CAT Seminar, November 2017.

• "The combinatorics of symmetric quotient rings," University of Kentucky CATS Seminar, November 2017.

• "Lattice paths inside shapes," New York Combinatorics Seminar, October 2017.

• "Lattice paths inside shapes," VCU, Richmond, VA, January 2017.

• "Conjectures for delta operator expressions," Equivariant Combinatorics Workshop, Montreal, June 2017.

• "Statistics on ordered multiset partitions," AMS Sectional Meeting, Athens, GA, March 2017.

  • Slides, handout

• "The Delta Conjecture," University of Washington Combinatorics Seminar, February 2016.

  • Slides, handout

• "The Delta Conjecture," CAGE Seminar, Philadelphia, November 2015.

• "Bijections for the Shi and Ish arrangements," AMS Sectional Meeting, Chicago, October 2015.

• "Generalized shuffle conjectures for the Garsia-Haiman delta operator," PhD Defense, UCSD, May 2015.

• "Tesler matrices and parking functions," UCLA Combinatorics Seminar, May 2015.

  • Slides, handout

• "Applications of elliptic curves," UCSD Food for Thought Seminar, May 2015.

• "Parking functions with undesirable spaces," AMS Sectional Meeting, Las Vegas, April 2015.

  • Slides, handout, Keynote presentation

• "Parking functions with undesirable spaces," Joint Math Meetings,  San Antonio, January 2015.

• "An extension of MacMahon's equidistribution theorem to ordered multiset partitions," Strathclyde Combinatorics Seminar, Glasgow, November 2014.

• "An extension of MacMahon's equidistribution theorem to ordered multiset partitions," FPSAC, Chicago, July 2014.

• "Two cases of an extended Shuffle Conjecture." UCSD Combinatorics Seminar, June 2014.

• "Schubert calculus," UCSD Food for Thought Seminar, December 2013.

• Permutation Patterns, Paris, July 2013.

• Advancement to candidacy, UCSD, May 2013.

• Grad Student Combinatorics Conference, University of Minnesota, April 2013.

• Senior project presentation, Washington University in St. Louis, June 2010.