Mohamed Omar


Department of Mathematics Email: m[lastname]@caltech.edu
California Institute of Technology Office: Sloan 358

Welcome to my website! I am a Harry Bateman Research Instructor in the Department of Mathematics at Caltech . I recently received my PhD in Mathematics from the University of California, Davis under the supervision of Jesús De Loera and partially supported by an NSERC PGS D doctoral grant. Before this, I completed the Double Honours program in Pure Mathematics and Combinatorics & Optimization (2006), and the Master's program in Combinatorics & Optimization (2007) under the supervision of Ian Goulden, both at the University of Waterloo. Here is my Curriculum Vitae

Research

Algebraic methods in Graph Theory and Discrete/Combinatorial Optimization.

Articles

  1. On Volumes of Permutation Polytopes, submitted (w/ Burggraf K., De Loera, J.)

  2. Strong Nonnegativity & Sums of Squares on Real Varieties, submitted (w/ Osserman, B.)
  3. On the Hardness of Counting and Sampling Center Strings (Journal Version), to appear in IEEE/ACM Transactions on Computational Biology and Bioinformatics (w/ Boucher, C.)
  4. Recognizing Graph Theoretic Properties with Polynomial Ideals., Electronic Journal of Combinatorics. Vol 17, R114 (2010) (w/ De Loera, J., Hillar, C., Malkin, P.)
  5. On the Hardness of Counting and Sampling Center Strings (Conference Version), In the proceedings of the Symposium on String Processing and Information Retrieval, SPIRE, pp. 128-135, (2010) (w/ Boucher, C.)
  6. Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers. Fifth Colloquium on Mathematics and Computer Science, Discrete Mathematics and Theoretical Computer Science, pp. 195-206 (2008) (w/ Eagle, C., Gao, Z., Panario, D., Richmond, B.)
  7. Asymptotics of Largest Components in Combinatorial Structures. Algorithmica. Vol. 46, Issue: 3-4. pp.493-503 (2006) (w/ Panario, D., Richmond, B., Whitely, J.)

Other Publications

Selected Presentations

Teaching

Caltech

UC Davis

University of Waterloo

Outreach/Enrichment

I am interested in and heavily involved with mathematics outreach, particularly at the high school level. My participation includes:

American Mathematics Competitions: Advisory Panel

The American Mathematics Competitions are premier high school math contests that serve as precursors for the selection of the USA International Mathematical Olympiad team. As a member of the Advisory Panel, I contribute problems, and edit and review tests.

Canada/USA Mathcamp: Graduate Student Mentor

In Summer 2011 I will be a Graduate Student Mentor at Canada/USA Mathcamp, an intensive 5-week-long summer program for outstandingly talented high school students. The program allows students to explore undergraduate and even graduate and research-level math topics in a vibrant and passionate environment. My role as a mentor is to work with other mentors in serving as an active mathematics teacher, residence counselor, and primary camp policy leader, setting the tone of the entire program.

Explore Math: Director of the Northern California ARML Team

Explore Math is an NSF VIGRE funded high school enrichment initiative organized and run solely by graduate students at UC Davis. ARML (American Regions Mathematics League) is a national mathematics competition for high school students held on the last weekend of May at four sites around the United States. I was the director for the program in 2010, and was the primary instructor for the Northern California ARML team in the Winter 2009 Quarter.

mathleague.org: Competition Writer

I write mathematics competitions for mathleague.org, a national program that provides various mathematics competitions to high school math circles. I am particularly involved with writing Sprint competitions: 30 problem multiple choice competitions akin to the AMC-10 and AMC-12 competitions run by the Mathematical Association of America (see AMC Mathematics Competitions).

In the past, I have been involved with Canadian Mathematics Competitions run by the Centre for Education in Mathematics & Computing.