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. Below is my work. Student co-authors are in orangered.

Any requests for non-research talks or outreach work can be sent here. Due to the volume of requests, all such engagements are subject to a consulting fee.


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

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

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


  1. Distinct Distances Between Points On A Variety And An Arbitrary Point Set
    in preparation, w/ Bryce McLaughlin
  2. Lattice Point Visibility On Power Functions
    submitted, 6 pp.
    w/ Pamela E. Harris
  3. Descent Polynomials
    submitted, 26 pp.
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
  4. Peaks on Graphs
    submitted, 11 pp.
    w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
  5. Sparse Neural Codes
    submitted, 12 pp.
    w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
  6. Neural Ideal Preserving Homomorphisms
    to appear, Journal of Pure and Applied Algebra, 13 pp.
    w/ R. Amzi Jeffs, Nora Youngs
  7. 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
  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. Recognizing Graph Theoretic Properties with Polynomial Ideals
    Electronic Journal of Combinatorics, 17(1), R114, 2010.
    w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
  15. 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
  16. Asymptotics of Largest Components in Combinatorial Structures
    Algorithmica 46 (3-4), pp. 493-503, 2006.
    w/ Daniel Panario, Bruce Richmond, Jacki Whitely


  1. New Perspectives on Flexibility in Simple Temporal Planning
    to appear, ICAPS, 18pp.
    w/ J. Boerkoel, A. Huang, L. Lloyd
  2. 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
  3. 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


  1. I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition
  2. to appear, PRIMUS, 2017.
    w/ Houssain El-Turkey, Gulden Karakok, Milos Savic, Gail Tang

  3. Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies
  4. Proceedings of the 20th Annual Conference on Research In Undergraduate Mathematics Education, 2017.
    w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang

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


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