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Department of Combinatorics & Optimization
University of Waterloo
200 University Avenue West
Waterloo, ON, N2L 3G1
Canada
Email: lcrew@uwaterloo.ca
I am an Assistant Professor at the University of Waterloo. My research is in algebraic combinatorics with a focus on using algebra in graph theory, and particularly the chromatic symmetric function. I earned my PhD from the University of Pennsylvania in 2020; my advisors were Jim Haglund and Greta Panova.
Due to severe long COVID, I was unable to work for almost two years between 2023 and 2025. I remain highly vulnerable to additional complications if I were to ever catch COVID again, and I appreciate efforts to help combat the spread of COVID and to help protect me and other similarly vulnerable people.
Pronouns: she/her
My papers are available on arXiv and on Google Scholar.
Here is a list of pairs of small graphs that have equal chromatic symmetric function, and their characteristics. This list was compiled by myself and Sophie Spirkl with a computer program, using the database of graphs provided by Brendan McKay on his homepage.
My wife Sophie Spirkl is an Associate Professor in the Department of Combinatorics & Optimization at the University of Waterloo.
Students:
PhD - Josephine Reynes (2021-2025) [co-supervised with Rowan Yeats]
Masters - Evan Haithcock (2021-2023), Laura Pierson (2023-2024) [co-supervised with Oliver Pechenik], Shao Yuan (Victor) Lin (2026-)
Undergraduate - William Chan (2021), Yongxing (Nick) Zhang (2022), Michael Xu (2023), Helena Devinyak (2026)
Preprints:
Decomposing Tournaments into Comparability Graphs with Pierre Aboulker, Julien Duron, Xinyue Fan, Hugo Jacob, Rémy Kimbrough, Hidde Koerts, Benjamin Moore, Sophie Spirkl, and Stéphan Thomassé. Submitted (2026).
Characterizing Large Clique Number in Tournaments with Xinyue Fan, Hidde Koerts, Benjamin Moore, and Sophie Spirkl. Submitted (2026).
e-basis Coefficients of Chromatic Symmetric Functions with Yongxing Zhang. In revision (2026).
Published and accepted papers:
The Kromatic Symmetric Function: A K-Theoretic Analogue with Oliver Pechenik and Sophie Spirkl.
Published by Canadian Mathematical Bulletin (2026).
On Prime Cayley Graphs with Maria Chudnovsky, Michal Cizek, Ján Mináč, Tung Nguyen, Sophie Spirkl, and Nguyên Tân.
Published by Journal of Combinatorics (2026).
Homogeneous Sets in Graphs and a Chromatic Multisymmetric Function with Evan Haithcock, Josephine Reynes, and Sophie Spirkl.
Published by Advances in Applied Mathematics (2024).
A Graph Polynomial from Chromatic Symmetric Functions with William Chan.
Published by Journal of Graph Theory (2023).
Plethysms of Chromatic and Tutte Symmetric Functions with Sophie Spirkl.
Published by Electronic Journal of Combinatorics (2022).
Published by Discrete Mathematics (2022).
Modular Relations of the Tutte Symmetric Function with Sophie Spirkl.
Published by Journal of Combinatorial Theory, Series A (2022).
Branching Rules for Splint Root Systems with Alexandre A. Kirillov and Yao-Rui Yeo.
Published by Journal of Algebras and Representation Theory (2022).
A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function with José Aliste-Prieto, Sophie Spirkl, and José Zamora.
Published by Electronic Journal of Combinatorics (2021).
A Complete Multipartite Basis for the Chromatic Symmetric Function with Sophie Spirkl.
Published by SIAM Journal on Discrete Mathematics (SIDMA) (2021).
Disproportionate Division with Bhargav Narayanan and Sophie Spirkl.
Published by Bulletin of the London Mathematical Society (2020).
A Deletion-Contraction Relation for the Chromatic Symmetric Function with Sophie Spirkl.
Published by European Journal of Combinatorics (2020).
Talks/Presentations:
The Kromatic Symmetric Function (Poster). Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (2023).
The Kromatic Symmetric Function (Slides). UC Davis Algebraic Geometry Seminar (2023)
The Kromatic Symmetric Function. Rutgers University Schubert Seminar (2023).
Chromatic Symmetric Functions: How to Study Graphs using Algebra, and Vice Versa (slides). Western University Special Seminar (2023).
Chromatic Multisymmetric Functions. York University Applied Algebra Seminar (2022).
A Graph Theoretic Approach to Plethysms of Symmetric Functions. University of Waterloo Algebraic Combinatorics Seminar (2022).
Graph Bases from the Chromatic Symmetric Function (Slides). AMS Western Sectional Meeting, Special Session on Graph Colorings (2022).
The Chromatic Symmetric Function: A Refinement of the Chromatic Polynomial (Slides). Illinois Institute of Technology Discrete Math Seminar (2022).
Graph Polynomials from Chromatic Symmetric Functions (Video/Slides). NTNU Algebraic and Combinatorial Perspectives in the Mathematical Sciences Seminar (2022).
A New Graph Polynomial from the Chromatic Symmetric Function (Slides Here). University of Waterloo Algebraic Graph Theory Seminar (2021).
Structural Properties of the Chromatic and Tutte Symmetric Functions (Slides Only). University of British Columbia Discrete Math Seminar (2021).
Identities of the Chromatic and Tutte Symmetric Functions (Slides Only). Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM, 2021).
The Tutte Symmetric Function (Slides Only). University of Waterloo Tutte Colloquium (2020).
Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. York University Applied Algebra Seminar (2020). (Slides)
Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. University of Waterloo Algebraic Combinatorics Seminar (2020).
Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions. University of Florida Combinatorics Seminar (2020).
A Deletion-Contraction Relation for the Chromatic Symmetric Function (and Slides). University of Albany Virtual Discrete Math 2-Day (2020).
A Deletion-Contraction Relation for the Chromatic Symmetric Function (Slides Only). Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM, 2019).
Teaching:
Fall 2025: MATH239 (see below)
Spring 2023: MATH239 and CO480 (see below)
Winter 2023: MATH239 (Introduction to Combinatorics)
Spring 2022: CO380 (Mathematical Discovery and Invention)
Winter 2022: MATH119 (Calculus 2 for Engineering)
Spring 2021: CO480 (History of Mathematics)
Winter 2021: MATH228 (Differential Equations for Physics and Chemistry)
Fall 2020: MATH115 (Linear Algebra for Engineering)
Reviewer for:
Mathematical Reviews, zbMath Open, FPSAC, EuroComb, LAGOS, Advances in Mathematics, International Math Research Notices, Advances in Applied Mathematics, Journal of Graph Theory, Annals of Combinatorics, Electronic Journal of Combinatorics, Discrete Mathematics, Discrete Applied Mathematics.
PhD thesis:
Vertex-Weighted Generalizations of Chromatic Symmetric Functions. Advisors: Jim Haglund and Greta Panova (University of Pennsylvania, 2020).
Master's thesis:
The Shuffle Conjecture. Advisor: Jim Haglund (University of Pennsylvania, 2017).
Bachelor's thesis:
On the characterization of the numbers n such that any group of order n has a given property P. Advisor: Thomas Haines (University of Maryland, College Park, 2015).
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