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. My articles are below.

  1. Peaks on Graphs
    in preparation
    w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
  2. Neural Ideal Preserving Homomorphisms
    in preparation
    w/ R. Amzi Jeffs, Nora Youngs
  3. A Proof of the Peak Polynomial Positivity Conjecture
    submitted, 7 pp
    w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
  4. Sparse Neural Codes
    submitted, 12 pp
    w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
  5. 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
  6. What makes a neural code convex?
    submitted, 28 pp
    w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
  7. Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies
  8. accepted, Research In Undergraduate Mathematics Education, 2016
    w/ Gulden Karakok, Milos Savic, Gail Tang

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

  11. Low Degree Nullstellensatz Certificates for 3-Colorability
    Electronic Journal of Combinatorics, 23(1), P1.6, 2016.
    w/ Bo Li, Benjamin Lowenstein
  12. Chromatic Bounds on Orbital Chromatic Roots
    Electronic Journal of Combinatorics, 21(4), P4.17, 2014.
    w/ Dae Hyun Kim, Alexander H. Mun
  13. Strong Nonnegatvity and Sums of Squares on Real Varieties
    Journal of Pure and Applied Algebra 217 (5), pp. 843-850, 2013.
    w/ Brian Osserman
  14. On Volumes of Permutation Polytopes
    Fields Institute Communications Vol. 69, Discrete Geometry and Optimization, pp. 55-77, 2013.
    w/ Katherine Burggraf, Jesus De Loera
  15. 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
  16. Applications of Convex and Algebraic Geometry to Graphs and Polytopes
    Ph.D. Thesis, Advisor: Jesus De Loera. UC Davis, 2011.
  17. Recognizing Graph Theoretic Properties with Polynomial Ideals
    Electronic Journal of Combinatorics, 17(1), R114, 2010.
    w/ Jesus De Loera, Peter N. Malkin
  18. 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
  19. This is the conference version of the journal paper listed above.

  20. 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
  21. Combinatorial Approaches to the Jacobian Conjecture
    Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.
  22. Asymptotics of Largest Components in Combinatorial Structures
    Algorithmica 46 (3-4), pp. 493-503, 2006.
    w/ Daniel Panario, Bruce Richmond, Jacki Whitely