Welcome to my academic page! I am an Associate Professor in the Department of Mathematics at Harvey Mudd College and the Joseph B. Platt Chair in Effective Teaching.
I am interested in seeing algebra come alive in discrete mathematics, primarily in combinatorics, graph theory and discrete/convex geometry. I am also interested in enumerative and geometric combinatorics. Below is my work.AWARDS
ARTICLES

Factorization Length Distribution For Affine Semigroups III: Moments and Modular Behavior of Factorization
to appear, Journal of the Australian Mathematics Society.
w/ Stephan Ramon Garcia, Christopher O'Neill  On Distinct Distances Between a Variety and a Point Set
to appear, Electronic Journal of Combinatorics.
w/ Bryce McLaughlin 
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 BSplines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
Linear Algebra and its Applications Vol. 608, pp. 6883, 2021.
w/ Albrecht Bottcher, Stephan Ramon Garcia, Christopher O'Neill  Counting Peaks on Graphs
Australasian Journal of Combinatorics, Vol. 75, Issue 2, pp. 174189, 2019.
w/ Alex DiazLopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio  Descent Polynomials
Discrete Mathematics, Vol. 342, pp. 16741686, 2019.
w/ Alex DiazLopez, Pamela E. Harris, Erik Insko, Bruce Sagan  Sparse Neural Codes
Involve, Vol. 12, No. 5, pp. 737754, 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.34703482, 2018.
w/ R. Amzi Jeffs, Nora Youngs  The qanalog of Kostant's partition function and the highest root of the classical Lie algebras
Australasian Journal Of Combinatorics , Vol 71, Issue 1, pp.6891, 2018.
w/ Pamela E. Harris, Erik Insko  A Proof of the Peak Polynomial Positivity Conjecture
Journal of Combinatorial Theory Series A, Vol 149, pp. 2129, 2017.
w/ Alex DiazLopez, Pamela E. Harris, Erik Insko  What makes a neural code convex?
SIAM Journal on Applied Algebra and Geometry, Vol 1, Issue 1, p. 222238, 2017.
w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs  Low Degree Nullstellensatz Certificates for 3Colorability
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. 843850, 2013.
w/ Brian Osserman  On The Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics Vol. 9 Issue 6, pp. 18431846, 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 (34), pp. 493503, 2006.
w/ Daniel Panario, Bruce Richmond, Jacki Whitely
CONFERENCE ARTICLES
 New Perspectives on Flexibility in Simple Temporal Planning
TwentyEighth 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 DiazLopez, 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. 128135, 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. 195206, 2008.
w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond
BOOKS/BOOK CHAPTERS
 Graph Theory Toward Undergraduate Research in Several Undergraduate Lectures
in preparation.  Number Theory Toward RSA Cryptography: in 10 undergraduate lectures
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  On Volumes of Permutation Polytopes
Fields Institute Communications, Discrete Geometry and Optimization, pp. 5577, 2013.
w/ Katherine Burggraf, Jesus De Loera
PEDAGOGY ARTICLES
 I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition PRIMUS, Vol. 29, Issue 1, pp. 82102, 2019.
 Preparing Students for the GRE Math Subject Test Math Focus, Oct/Nov Issue, p.2425, 2018. w/ Ivan B. Ventura
 Pedagogical Practices for Fostering Mathematical Creativity and ProofBased Courses: Three Case Studies Proceedings of the 20th Annual Conference on Research In Undergraduate Mathematics Education, pp. 14181424, 2017.
 Pedagogical Practices for Fostering Mathematical Creativity in TertiaryLevel ProofBased Courses. Proceedings of the 10th Biannual Conference on Mathematical Creativity and Giftedness, pp. 130135, 2017.
 Tame The GRE Math Subject Test Math Horizons, Vol. 24, Issue 2, p.2829, 2016.
w/ Houssain ElTurkey, Gulden Karakok, Milos Savic, Gail Tang
w/ Emily CilliTurner, Houssain ElTurkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang
w/ Emily CilliTurner, Houssain ElTurkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang
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.