# Research Statement

### My research is in the field of algebraic combinatorics. I am mostly interested in combinatorial problems related to reflection groups or their associated Artin groups.

# My Google Scholar page

# Preprints and papers

- October 2008 - An alternating sum of alternating sign matrices - Rose Hulman Undergraduate Mathematics Journal
- August 2011 - (with J. Striker) Promotion and Rowmotion - European Journal of Combinatorics
- March 2012 - (with M. Visontai) Stable multivariate W-Eulerian polynomials - Journal of Combinatorial Theory Series A
- July 2012 - (with H. Thomas) Cyclic Symmetry of the Scaled Simplex - Journal of Algebraic Combinatorics
- May 2013 - (with D. Armstrong and B. Rhoades) Rational associahedra and noncrossing partitions - Formal Power Series and Algebraic Combinatorics DMTCS Proceedings 2013 - Electronic Journal of Combinatorics
- October 2014 - (with C. Berg and M. Zabrocki) Symmetries on the lattice of k-bounded partitions - Annals of Combinatorics
- February 2015 - Associahedra have the non-face-leaving property - European Journal of Combinatorics
- March 2015 - (with T. Gobet) Noncrossing partitions and Bruhat order - European Journal of Combinatorics
- Jul 2015 - (with A. Schilling, N. Thiéry, G. White) Braid moves in commutation classes of the symmetric group - European Journal of Combinatorics
- August 2015 - (with M. Thiel) Strange Expectations - Journal of Algebraic Combinatorics
- October 2015 - (with C. Hohlweg and P. Nadeau) Automata, reduced words, and Garside shadows in Coxeter groups - Journal of Algebra
- December 2015 - (with H. Thomas) Sweeping up Zeta - Selecta Mathematica
- August 2017 - (with Z. Hamaker, R. Patrias, and O. Pechenik) Doppelgängers: Bijections of Plane Partitions - International Mathematics Research Notices
- January 2018 - (with H. Thomas) Rowmotion in slow motion - Proceedings of the London Math Society
- April 2018 - (with H. Mühle) Tamari Lattices for Parabolic Quotients of the Symmetric Group - submitted
- May 2018 - (with H. Thomas) Independence Posets - Journal of Combinatorics (special issue in honor of Jeff Remmel)
- May 2018 - Planted Brussels Sprouts (after Ji-Propp) - Journal of Integer Sequences
- October 2018 - (with C. Stump and H. Thomas) Cataland: Why the Fuss? - submitted
- November 2018 - (with M. Thiel) Strange Expectations and the Winnie-the-Pooh Problem - submitted
- Jan 2019 - (with J. McCammond and H. Thomas) Fixed Points of Parking Functions - submitted
- Feb 2019 - Reflexponents - submitted
- Feb 2019 - Fixed Points of Parking Functions - submitted
- April 2019 - (with H.Mühle and P. Nadeau) k-Indivisible Noncrossing Partitions - submitted

# Abstracts for Formal Power Series and Algebraic Combinatorics (FPSAC) - DMTCS Proceedings

- FSPAC 2012 - (with M. Visontai) Les polynômes eulériens stables de type B
- FSPAC 2012 - (with J. Striker) Promotion and Rowmotion
- FPSAC 2013 - (with D. Armstrong and B. Rhoades) Rational Catalan combinatorics: the associahedron
- FSPAC 2014 - Bijactions in Cataland
- FPSAC 2015 - (with Z. Hamaker) Subwords and Plane Partitions
- FPSAC 2015 - (with H. Mühle) Tamari Lattices for Parabolic Quotients of the Symmetric Group
- FPSAC 2016 - (with M. Thiel) Strange Expectations and Simultaneous Cores
- FPSAC 2016 - (with C. Stump and H. Thomas) Cataland: Why
the Fuss?
- FPSAC 2017 - (with H. Thomas) Sweeping up Zeta
- FPSAC 2018 - (with M. Thiel) Winnie the Pooh and the Strange Expectations

# Other Writing

- December 2012 - Rational Catalan Combinatorics AIM Outline
- August 2013 - Thesis - Cataland
- March 2019 - (summary of the BIRS workshop with A. Morales, I. Pak, G. Panova, and D. Romik) Asymptotic algebraic combinatorics

# Presentations

- March 2010 - University of Minnesota - Combinatorics Seminar - Cyclic Sieving in Young's Lattice
- 15 April 2011 - University of Minnesota - Combinatorics Seminar - Promotion and Rowmotion
- 28 June 2011 - Institut Camille Jordan - Promotion et Rowmotion (French) - Promotion and Rowmotion (English)
- 21 January 2012 - Combinatorial Algebra Meets Algebraic Combinatorics (Montréal, Canada) - Cyclic Symmetry in Young's Lattice
- 14 February 2012 - York University - Applied Math Seminar - Suter's Surprising Cyclic Symmetry
- 2 March 2012 - University of Miami - Promotion and Rowmotion
- 10 March 2012 - AMS Special Session on Combinatorics: Algebraic and Geometric (Tampa, Florida) - Towards a uniform description of a bijection between nonnesting and noncrossing partitions
- 11 July 2012 - Summer School on Algebraic and Enumerative Combinatorics (S. Miguel de Seide, Portugal) - Cyclic Symmetry of the Scaled Simplex (for 3D, view in Chrome)
- 31 July 2012 - Formal Power Series and Algebraic Combinatorics (Nagoya, Japan) - Promotion and Rowmotion
- 16 November 2012 - University of Minnesota - Noncrossing and Nonnesting Partitions for Parabolic Quotients
- 30 August 2013 - University of Minnesota - Thesis defense: Cataland
- 20 September 2013 - Laboratoire de Combinatoire et d'Informatique Mathématique - Combinatorics Seminar - Cataland
- 18 November 2013 - York University - Applied Math Seminar - Cataland
- October 2013 - Freie Universität Berlin - Discrete Geometry Seminar - Cataland
- 10 December 2013 - North Dakota State University - Department Colloquium - Cataland
- January 2014 - Combinatorial Algebra Meets Algebraic Combinatorics (Halifax, Canada) - Cataland
- 7 February 2014 - Laboratoire de Combinatoire et d'Informatique Mathématique - Combinatorics Seminar - Reduced Words and Plane Partitions in Type B
- 11 April 2014 - Laboratoire de Combinatoire et d'Informatique Mathématique - Combinatorics Seminar - Why the Fuss?
- 16 January 2015 - Laboratoire de Combinatoire et d'Informatique Mathématique - Combinatorics Seminar - Cristaux et l'Ordre Faible
- 23 January 2015 - Combinatorial Algebra Meets Algebraic Combinatorics (Kingston, Canada) - Why the Fuss? (transcript)
- 11 March 2015 - Sage Days 64 (University of California, Davis) - Why the Fuss?
- March 2015 - AIM Workshop: Dynamical Algebraic Combinatorics (San Jose, California) - Catland
- March 2015 - Institut Camille Jordan - Why the Fuss?
- April 2015 - Institut Camille Jordan - Why the Fuss?
- July 2015 - Formal Power Series and Algebraic Combinatorics (Daejeon, South Korea) - Subwords and Plane Partitions
- December 2015 - University of California, San Diego - Combinatorics Seminar - Sweeping up Zeta
- January 2016 - Massachusetts Institute of Technology - Combinatorics Seminar - Sweeping up Zeta
- January 2016 - Brandeis University - Special Seminar - Why the Fuss?
- March 2016 - University of California, Davis - Combinatorics Seminar - Sweeping up Zeta
- July 2016 - Formal Power Series and Algebraic Combinatorics (Vancouver, Canada)- Cataland - Why the Fuss?
- October 2016 - University of California, Santa Barbara - Discrete Geometry and Combinatorics Seminar - Sweeping up Zeta
- January 2017 - University of Massachusetts Amherst - Sweeping up Zeta
- January 2017 - The College of William and Mary - Sweeping up Zeta
- February 2017 - University of California, Santa Barbara - Discrete Geometry and Combinatorics Seminar - Doppelgängers: Bijections of Plane Partitions
- February 2017 - California State University, Fresno - Sweeping up Zeta
- February 2017 - The University of Texas at Dallas - Sweeping up Zeta
- May 2017 - The 2017 Midwest Combinatorics Conference, Minneapolis, Minnesota - Sweeping up Zeta
- June 2017 - University of California, Santa Barbara - Topology seminar - Why the Fuss?
- September 2017 - The University of Texas at Dallas - Algebra and Combinatorics Seminar - Three lectures on Coxeter-Catalan theory
- October 2017 - Haverford College - Sweeping up Zeta
- October 2017 - Combinatorics, Algebra, and Geometry seminar co-organized by Swarthmore College, Drexel University, the University of Pennsylvania, and Haverford College. - Doppelgängers
- January 2018 - The Joint Mathematics Meetings, Special Session in Honor of Dennis Stanton, San Diego - Winnie-the-Pooh and the Strange Expectations
- February 2018 - Texas A&M, Algebra and Combinatorics Seminar - Fixed Points of Parking Functions
- March 2018 - The University of Texas at Dallas - Nonlinear Analysis and Dynamical Systems Seminar - Dynamical Algebraic Combinatorics
- March 2018 - ALGECOM: Algebra, Geometry, and Combinatorics Day, University of Michigan - Fixed Points of Parking Functions
- July 2018 - SageDays@ICERM: Combinatorics and Representation Theory - ICERM, Brown University - Full Twist Presentations
- September 2018 - The University of Texas at Dallas - Algebra and Combinatorics Seminar - Full Twist Presentations
- September 2018 - CRM 50th anniversary conference: Algèbre et combinatoire au LaCIM, CRM, Montréal - Full Twist Presentations
- March 2019 - The University of Texas at Dallas - Algebra and Combinatorics Seminar - Reflexponents
- March 2019 - Talk by Dr. Kevin Williams - AMS Special Session (Hawaii)- Mathematical clarity versus an entrenched, out-of-touch bureaucracy: How we reformed a small well-run medical match -- and then the largest but badly run medical match.
- June 2019 - Canadian Discrete and Algorithmic Mathematics Conference - Simon Fraser University, Vancouver, Canada - Reflexponents
- June 2019 - Enumerative and analytic combinatorics seminar, Institut de Recherche en Informatique Fondamentale (IRIF) - Université Paris Diderot, Paris, France - Reflexponents
- June 2019 - Séminaire Combinatoire du Plateau de Saclay - Laboratoire d'informatique de l'École polytechnique (LIX), Paris, France - Independence Posets
- June 2019 - Combinatorics seminar - L'Institut Camille Jordan, Université Lyon 1, Lyon, France - Reflexponents
- July 2019 - Formal Power Series and Algebraic Combinatorics (Ljubljana, Slovenia) - Combinatorics of the ``Coincidental'' Reflection Groups (for Vic Reiner)
- September 2019 - 10th Annual Discrete Geometry and Algebriac Combinatorics Confrence (South Padre Island, TX) - Fixed Points of Parking Functions
- October 2019 - University of Washington, Seattle - Combinatorics Seminar - Fixed Points of Parking Functions

# Code

- 2012 - Mathematica Notebook for Cyclic Symmetry of the Scaled Simplex - View Notebook in HTML
- 2012 - Mathematica Notebook for Computing Regions with Zaslavasky's Theorem - View Notebook in HTML
- 2012 - GAP code for Confirming Theorem 1.2 of Reflexponents for primitive irreducible complex reflection groups - Data file supporting T. Douvropoulos's Galois twist conjecture