Research

Recorded talks

• Rotation-invariant web bases from hourglass plabic graphs and symmetrized six-vertex configurations, at the Institute for Pure and Applied Mathematics, April 2024

• A dynamic duo - Alternating sign matrices and plane partitions, at the Graduate Online Combinatorics Colloquium, February 2023.

• Promotion, rowmotion, rotation, and webs, at AlCoVE 2022.

• Promotion and rowmotion – an ocean of notions, at the BIRS Dynamical Algebraic Combinatorics Workshop, October 2020.

Publications (by topic)

Webs:

• Joint work with Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, and Joshua P. Swanson: Web bases in degree two from hourglass plabic graphs (submitted).

• Joint work with Chris Fraser, Rebecca Patrias, and Oliver Pechenik: Web invariants for flamingo Specht modules (submitted).

• Joint work with Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, and Joshua P. Swanson: Rotation-invariant web bases from hourglass plabic graphs (submitted).

• Joint work with Rebecca Patrias and Oliver Pechenik: A web basis of invariant polynomials from noncrossing partitions published in Advances in Mathematics (2022).

Dynamical algebraic combinatorics:

• Joint work with Ashleigh Adams, Jennifer Elder, Nadia Lafrenière, Erin McNicholas, and Amanda Welch: Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database (submitted).

• Joint work with Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, and Joshua P. Swanson: Promotion permutations for tableaux (submitted).

• Joint work with Joseph Bernstein and Corey Vorland: P-strict promotion and Q-partition rowmotion: the graded case published in European Journal of Combinatorics (2024).

• Joint work with Jennifer Elder, Nadia Lafrenière, Erin McNicholas, and Amanda Welch: Homomesies on permutations - an analysis of maps and statistics in the FindStat database published in Mathematics of Computation (2024).

• Joint work with Jennifer Elder, Nadia Lafrenière, Erin McNicholas, and Amanda Welch: Toggling, rowmotion, and homomesy on interval-closed sets  published in Journal of Combinatorics (2023).

• Joint work with Christian Gaetz, Oliver Pechenik, and Joshua Swanson: Curious cyclic sieving on increasing tableaux, published in Enumerative Combinatorics and Applications (2022).

• Joint work with Joseph Bernstein and Corey Vorland: P-strict promotion and B-bounded rowmotion, with applications to tableaux of many flavors, published in Combinatorial Theory (2021).

• Joint work with Kevin Dilks and Corey Vorland: Rowmotion and increasing labeling promotion, published in Journal of Combinatorial Theory Series A (2019).

• Rowmotion and generalized toggle groups, published in Discrete Math Theoretical Computer Science (2018).

• Dynamical algebraic combinatorics: promotion, rowmotion, and resonance, published in Notices of the American Mathematical Society (2017).

• Joint work with Kevin Dilks and Oliver Pechenik: Resonance in orbits of plane partitions and increasing tableaux, published in Journal of Combinatorial Theory Series A (2017).

• The toggle group, homomesy, and the Razumov-Stroganov correspondence, published in the Electronic Journal of Combinatorics (2015).

• Joint work with Nathan Williams: Promotion and rowmotion, published in the European Journal of Combinatorics (2012).

Alternating sign matrices and plane partitions (bijections):

• Joint work with Daoji Huang: A pipe dream perspective on totally symmetric self-complementary plane partitions, published in Forum of Math, Sigma (2024). 

• Permutation totally symmetric self-complementary plane partitions, published in Annals of Combinatorics (2018).

• Joint work with Dylan Heuer, Chelsey Morrow, Ben Noteboom, Sara Solhjem, and Corey Vorland: Chained permutations and alternating sign matrices - inspired by three-person chess, published in Discrete Mathematics (2017).

• A direct bijection between descending plane partitions with no special parts and permutation matrices, published in Discrete Mathematics (2011).

• A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux, published in Advances in Applied Mathematics (2011).

Alternating sign matrices and plane partitions (polytopes):

• Joint work with Sara Solhjem and Dylan Heuer: On nu faces of partial alternating sign matrix polytopes (submitted).

• Joint work with Vincent Holmlund: Totally symmetric self-complementary plane partition polytopes (submitted).

• Joint work with Dylan Heuer: Partial permutation and alternating sign matrix polytopes, published in SIAM Journal on Discrete Math (2022).

• Joint work with Sara Solhjem: Sign matrix polytopes from Young tableaux, published in Linear Algebra and its Applications (2019).

• Joint work with Karola Meszaros and Alejandro Morales: On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope, published in Discrete and Computational Geometry (2019).

• The alternating sign matrix polytope, published in the Electronic Journal of Combinatorics (2009).

• My PhD thesis: Poset and polytope perspectives on alternating sign matrices (2008).

Selected Slides

• Slides from my 2023 talk at Dagstuhl: Two new bijections on six-vertex configurations

• Presentation and Activities for my 2021 UMN combinatorics seminar talk: P-strict promotion and B-bounded rowmotion

• Slides from my 2019 talks at the MAA North Central Fall Section Meeting and University of Winnipeg Colloquium: Mind-boggling toggling

• Slides from my 2018 lecture series at Sungkyunkwan University in Suwon, South Korea:

  • • Dynamical algebraic combinatorics: Cyclic sieving and homomesy

    • Dynamical algebraic combinatorics: Resonance

    • Poset and permutation perspectives on alternating sign matrices and certain plane partitions

• Slides from my 2016 talk at the University of Minnesota Combinatorics Seminar: Resonance in orbits of plane partitions and increasing tableaux

• Slides from my talk at the 2015 Dynamical algebraic combinatorics AIM workshop: Toggle group actions, applications, and abstraction.