Mohamed Omar

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

- Algebraic and Geometric Methods in Applied Discrete Mathematics

Proceedings of the AMS Special Session volume,**Contemporary Mathematics**

w/ Heather Harrington, Matthew Wright - On Volumes of Permutation Polytopes

**Fields Institute Communications**, Discrete Geometry and Optimization, pp. 55-77, 2013.

w/ Katherine Burggraf, Jesus De Loera

- Peaks on Graphs

in preparation

w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio - Neural Ideal Preserving Homomorphisms

submitted, 13 pp.

w/ R. Amzi Jeffs, Nora Youngs - Sparse Neural Codes

submitted, 12 pp

w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs - 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 - 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 - 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 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 -
Applications of Convex and Algebraic Geometry to Graphs and Polytopes

Ph.D. Thesis, Advisor: Jesus De Loera. UC Davis, 2011. -
Recognizing Graph Theoretic Properties with Polynomial Ideals

**Electronic Journal of Combinatorics**, 17(1), R114, 2010.

w/ Jesus De Loera, Peter N. Malkin - 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 - 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 -
Combinatorial Approaches to the Jacobian Conjecture

Master's Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007. - Asymptotics of Largest Components in Combinatorial Structures

**Algorithmica**46 (3-4), pp. 493-503, 2006.

w/ Daniel Panario, Bruce Richmond, Jacki Whitely

- Preparing Students for the GRE Math Subject Test in preparation
- I Felt Like a Mathematician: Combining Challenging Theorems with Creative Effort and Metacognition submitted, 12 pp.
- Pedagogical Practices for Fostering Mathematical Creativity and Proof-Based Courses: Three Case Studies accepted,
- Tame The GRE Math Subject Test

w/ Houssain El-Turkey, Gulden Karakok, Milos Savic, Gail Tang

w/ Emily Cilli-Turner, Houssain El-Turkey, Gulden Karakok, David Plaxco, Milos Savic, Gail Tang