Mohamed Omar




Welcome to my website! I am an Assistant Professor in the Department of Mathematics at Harvey Mudd College.

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.

I am also very interested in the role creativity plays in mathematics education. I am part of a 6-person Creativity Research Group team that aims to infuse creativity throughout math education in order to obliterate math phobia and dismantle underrepresentation in mathematics.


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

  2. On Volumes of Permutation Polytopes
    Fields Institute Communications, Discrete Geometry and Optimization, pp. 55-77, 2013.
    w/ Katherine Burggraf, Jesus De Loera


  1. Descent Polynomials
    in preparation
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
  2. New Perspectives on Flexibility in Simple Temporal Planning
    in preparation
    w/ J. Boerkoel, A. Huang, L. Lloyd
  3. Peaks on Graphs
    submitted, 11 pp.
    w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
  4. Neural Ideal Preserving Homomorphisms
    submitted, 13 pp.
    w/ R. Amzi Jeffs, Nora Youngs
  5. Sparse Neural Codes
    submitted, 12 pp
    w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
  6. The q-analog of Kostant's partition function and the highest root of the classical Lie algebras
    submitted, 21 pp
    w/ Pamela E. Harris, Erik Insko
  7. A Proof of the Peak Polynomial Positivity Conjecture
    to appear, Formal Power Series and Algebraic Combinatorics 2017
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
  8. 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
  9. 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
  10. Low Degree Nullstellensatz Certificates for 3-Colorability
    Electronic Journal of Combinatorics, 23(1), P1.6, 2016.
    w/ Bo Li, Benjamin Lowenstein
  11. Chromatic Bounds on Orbital Chromatic Roots
    Electronic Journal of Combinatorics, 21(4), P4.17, 2014.
    w/ Dae Hyun Kim, Alexander H. Mun
  12. Strong Nonnegatvity and Sums of Squares on Real Varieties
    Journal of Pure and Applied Algebra 217 (5), pp. 843-850, 2013.
    w/ Brian Osserman
  13. 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
  14. Applications of Convex and Algebraic Geometry to Graphs and Polytopes
    Ph.D. Thesis, Advisor: Jesus De Loera. UC Davis, 2011.
  15. Recognizing Graph Theoretic Properties with Polynomial Ideals
    Electronic Journal of Combinatorics, 17(1), R114, 2010.
    w/ Jesus De Loera, Peter N. Malkin
  16. On The Hardness of Counting and Sampling Center Strings
    Proceedings of the 17th Annual Symposium on String Processing and Information Retrieval, pages 128-135, 2010.
    w/ Christina Boucher
  17. 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
  18. Combinatorial Approaches to the Jacobian Conjecture
    Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.
  19. Asymptotics of Largest Components in Combinatorial Structures
    Algorithmica 46 (3-4), pp. 493-503, 2006.
    w/ Daniel Panario, Bruce Richmond, Jacki Whitely


  1. Preparing Students for the GRE Math Subject Test
  2. submitted, 4 pp.
    w/ Ivan Ventura

  3. I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition
  4. submitted, 12 pp.
    w/ Houssain El-Turkey, Gulden Karakok, Milos Savic, Gail Tang

  5. Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies
  6. accepted, Research In Undergraduate Mathematics Education, 2017
    w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang

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