Welcome to my academic page! I'm a professor in the Department of Mathematics and Statistics at York University in my hometown of Toronto, Canada.

I like when polynomials are used to do discrete math. It's as simple as that. Below is my work.

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RECENT AWARDS

AMS Claytor-Gilmer Fellowship (Inaugural, National Research Award)

Karen EDGE Fellowship (Inaugural, National Research Award)

Henry L. Alder Award (National Teaching Award)

JOURNAL ARTICLES

• Growth Rates of Permutations with a Given Descent Word
  submitted, 18 pp.
  w/ Justin Troyka
• Permutations with a Given X-Descent Set
  submitted, 12 pp.
  
• Partition Rank and Partition Lattices
  to appear in Order, 25 pp.
  
• Sets Avoiding Full-Rank Three-Point Patterns in (F_q^n)^k Are Exponentially Small
  Australasian Journal of Combinatorics, Vol 85(3), pp. 423-429, 2023.
  
• Burning Graph Classes
  Graphs and Combinatorics, Vol 38(4), Article 121, 2022.
  w/ Vibha Rohilla
• On Distinct Distances Between a Variety and a Point Set
  Electronic Journal of Combinatorics, Vol. 29(3), P3.21, 2022.
  w/ Bryce McLaughlin
• Factorization Length Distribution For Affine Semigroups III: Modular Equidistribution for Numerical Semigroups with Arbitrarily Many Generators
  Journal of the Australian Mathematical Society Vol. 113(1), pp. 21-35, 2022.
  w/ Stephan Ramon Garcia, Christopher O'Neill, Timothy Wesley
• Factorization Length Distribution For Affine Semigroups II: Asymptotic Behavior for Numerical Semigroups with Arbitrarily Many Generators
  Journal of Combinatorial Theory, Series A Vol. 178, 105358, 2021.
  w/ Stephan Ramon Garcia, Christopher O'Neill, and Samuel Yih
• Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
  Linear Algebra and its Applications Vol. 608, pp. 68-83, 2021.
  w/ Albrecht Bottcher, Stephan Ramon Garcia, Christopher O'Neill
• Counting Peaks on Graphs
  Australasian Journal of Combinatorics, Vol. 75, Issue 2, pp. 174-189, 2019.
  w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
• Descent Polynomials
  Discrete Mathematics, Vol. 342, pp. 1674-1686, 2019.
  w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
• Sparse Neural Codes
  Involve, Vol. 12, No. 5, pp. 737-754, 2019.
  w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
• Lattice Point Visibility On Power Functions
  INTEGERS, Vol. 18, A90, 2018.
  w/ Pamela E. Harris
• Neural Ideal Preserving Homomorphisms
  Journal of Pure and Applied Algebra, Vol 222, Issue 11, pp.3470-3482, 2018.
  w/ R. Amzi Jeffs, Nora Youngs
• The q-analog of Kostant's partition function and the highest root of the classical Lie algebras
  Australasian Journal Of Combinatorics , Vol 71, Issue 1, pp.68-91, 2018.
  w/ Pamela E. Harris, Erik Insko
• A Proof of the Peak Polynomial Positivity Conjecture
  Journal of Combinatorial Theory Series A, Vol 149, pp. 21-29, 2017.
  w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
• What makes a neural code convex?
  SIAM Journal on Applied Algebra and Geometry, Vol 1, Issue 1, p. 222-238, 2017.
  w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
• Low Degree Nullstellensatz Certificates for 3-Colorability
  Electronic Journal of Combinatorics, 23(1), P1.6, 2016.
  w/ Bo Li, Benjamin Lowenstein
• Chromatic Bounds on Orbital Chromatic Roots
  Electronic Journal of Combinatorics, 21(4), P4.17, 2014.
  w/ Dae Hyun Kim, Alexander H. Mun
• Strong Nonnegatvity and Sums of Squares on Real Varieties
  Journal of Pure and Applied Algebra 217 (5), pp. 843-850, 2013.
  w/ Brian Osserman
• On Volumes of Permutation Polytopes
  Fields Institute Communications, Discrete Geometry and Optimization, pp. 55-77, 2013.
  w/ Katherine Burggraf, Jesus De Loera
• On The Hardness of Counting and Sampling Center Strings
  IEEE/ACM Transactions on Computational Biology and Bioinformatics Vol. 9 Issue 6, pp. 1843-1846, 2012.
  w/ Christina Boucher
• Recognizing Graph Theoretic Properties with Polynomial Ideals
  Electronic Journal of Combinatorics, 17(1), R114, 2010.
  w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
• Asymptotics of Largest Components in Combinatorial Structures
  Algorithmica 46 (3-4), pp. 493-503, 2006.
  w/ Daniel Panario, Bruce Richmond, Jacki Whitely

CONFERENCE ARTICLES

• New Perspectives on Flexibility in Simple Temporal Planning
  Twenty-Eighth International Conference on Automated Planning and Scheduling 2018, 18pp., 2018.
  w/ Jim Boerkoel, Amy Huang, Liam Lloyd
• A Proof of the Peak Polynomial Positivity Conjecture
  Formal Power Series and Algebraic Combinatorics 2017, 10pp., 2017. w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
• On The Hardness of Counting and Sampling Center Strings
  Proceedings of the 17th Annual Symposium on String Processing and Information Retrieval, pp. 128-135, 2010.
  w/ Christina Boucher
• Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers
  Discrete Mathematics and Theoretical Computer Science, Fifth Colloquium on Math and Computer Science, pp. 195-206, 2008.
  w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond

BOOKS

• Graph Theory You Need Before Undergrad Research: in 8 undergrad lectures
  Amazon CreateSpace, 2021.

• Number Theory Toward RSA Cryptography: in 10 undergraduate lectures
  Amazon CreateSpace, 2017.

• Algebraic and Geometric Methods in Applied Discrete Mathematics
  Contemporary Mathematics, Proceedings of the AMS Special Session, Volume 685, 2017.
  w/ Heather Harrington, Matthew Wright

OTHER ARTICLES

• I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition
PRIMUS, Vol. 29, Issue 1, pp. 82-102, 2019.
w/ Houssain El-Turkey, Gulden Karakok, Milos Savic, Gail Tang
• Preparing Students for the GRE Math Subject Test
Math Focus, Oct/Nov Issue, p.24-25, 2018. w/ Ivan B. Ventura
• Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies
Proceedings of the 20th Annual Conference on Research In Undergraduate Mathematics Education, pp. 1418-1424, 2017.
w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang

• Pedagogical Practices for Fostering Mathematical Creativity in Tertiary-Level Proof-Based Courses.
Proceedings of the 10th Biannual Conference on Mathematical Creativity and Giftedness, pp. 130-135, 2017.
w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang

• Tame The GRE Math Subject Test
Math Horizons, Vol. 24, Issue 2, p.28-29, 2016.

THESES

• Applications of Convex and Algebraic Geometry to Graphs and Polytopes
  Ph.D. Thesis. Advisor: Jesus De Loera. UC Davis, 2011.
• Combinatorial Approaches to the Jacobian Conjecture
  Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.