Mohamed Omar
Department of Mathematics
California Institute of Technology
Mathematics 253-37, Pasadena, California, USA, 91125
(626)-726-1142
Citizenship: Canada
momar@caltech.edu
http://www.its.caltech.edu/∼momar
Employment
• Harry Bateman Research Instructor
Dept. of Mathematics, Caltech, Sept. 2011 - Present
– Postdoctoral fellow in mathematics.
– Taught various undergraduate & graduate courses, and organized department’s
combinatorics seminar.
• Academic Coordinator for Canada/USA Mathcamp
Mathematics Foundation of America, Jun 2012 - Aug 2012
– Coordinated and scheduled academics for 5 week program consisting of over 100
mathematics courses.
– Coordinated new teacher mentoring program, college selection program, and project
presentation fair.
• Director for ARML program in Explore Math
Dept. of Mathematics, University of California, Davis, Jan 2010 - Jun 2010
– Directed competition component of UC Davis Explore Math Program, funded by the
UC Davis College of Letters & Sciences, and supported by NSF VIGRE grants.
– Managed undergraduate seminar credit course in high school teaching, and curriculum
development for team training.
Education
• Ph.D., Mathematics
Thesis: Applications of Convex and Algebraic Geometry to Graphs and Polytopes
University of California, Davis, Jun. 2011.
Advisor: Jesús De Loera
• M.Math., Combinatorics & Optimization
University of Waterloo, Oct. 2007
Advisor: Ian P. Goulden
• B.Math., Dean’s Honour List
Pure Mathematics/Combinatorics & Optimization
Double Honours Co-operative Program
University of Waterloo, Jun. 2006
Research Interests
• Algebraic methods in Graph Theory and Discrete/Combinatorial Optimization
Articles
1. On Volumes of Permutation Polytopes, to appear in Fields Institute Communications
Series on Discrete Geometry & Optimization (w/ Burggraf, K., De Loera, J.)
2. Strong Nonnegativity & Sums of Squares on Real Varieties, to appear in Journal of
Pure and Applied Algebra. (w/ Osserman, B.)
3. On the Hardness of Counting and Sampling Center Strings (Journal Version), to
appear in IEEE/ACM Transactions on Computational Biology & Bioinformatics (w/
Boucher, C.)
4. On the Hardness of Counting and Sampling Center Strings (Conference
Version), String Processing and Information Retrieval Symposium (SPIRE) 2010,
pp.128-135 (w/ Boucher, C.)
5. Recognizing Graph Theoretic Properties with Polynomial Ideals. Electronic
Journal of Combinatorics. Vol. 17, R114 (2010) (w/ De Loera, J., Hillar, C., Malkin, P.)
6. Distribution of the Number of Encryptions in Revocation Schemes for Stateless
Receivers. 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.)
Teaching Experience
• Instructor for Calculus
Dept. of Mathematics, Caltech, Sept 2012 - Dec 2012
• Instructor for Algebra I (High School)
Art of Problem Solving, Sept 2012 - Feb 2013
• Instructor for Introduction to Discrete Math I
Dept. of Mathematics & Dept. of Computer Science, Caltech, Sept 2012 - Dec 2012
• Instructor for Geometric Combinatorics (Graduate Class)
Dept. of Mathematics, Caltech, April 2012 - June 2012
• Instructor for Introduction to Discrete Math II
Dept. of Mathematics & Dept. of Computer Science, Caltech, Jan 2012 - Mar 2012
• Instructor for Introduction to Discrete Math I
Dept. of Mathematics & Dept. of Computer Science, Caltech, Sept. 2011 - Dec. 2011
• Instructor for Canada/USA Mathcamp
Mathematics Foundation of America, Jun 2011 - Aug 2011
• Discussion Instructor for Modern Linear Algebra
Dept. of Mathematics, University of California, Davis, Jan. 2011 - Mar. 2011
• Instructor for Combinatorics
Dept. of Mathematics, University of California, Davis, Jun. 2010 - Sept. 2010
• Instructor for Combinatorics
Dept. of Mathematics, University of California, Davis, Jun. 2009 - Aug. 2009
• Instructor for ARML program in Explore Math Outreach Program
Dept. of Mathematics, University of California, Davis, Jan. 2009 - Mar. 2009
• Discussion Instructor for Modern Algebra
Dept. of Mathematics, University of California, Davis, Apr. 2008 - Jun. 2008
• Discussion Instructor for Integral Calculus
Dept. of Mathematics, University of California, Davis, Sept. 2007 - Mar. 2008
• Discussion Instructor for Calculus II
Dept. of Combinatorics & Optimization, University of Waterloo, May 2007 - Aug. 2007
• Discussion Instructor for Linear Algebra for Engineers
Dept. of Combinatorics & Optimization, University of Waterloo, Jan. 2007 - Apr. 2007
• Discussion Instructor for Discrete Math for Engineers
Dept. of Combinatorics & Optimization, University of Waterloo, Sept. 2006 - Dec. 2006
Awards, Grants & Honours
• Dean’s Prize - Division of Mathematical & Physical Sciences, UC Davis, 2011
• Yueh-Jing Lin Scholarship in Mathematics, UC Davis Mathematics, 2011
• UC Davis Mathematics Block Grant, 2011
• Alice Leung Research Scholarship in Mathematics, 2010
• UC Davis Mathematics Block Grant, 2007-2009
• NSERC Postgraduate Doctoral Scholarship, Tenure Abroad, 2007-2010
• NSERC Alexander Graham Bell Canada Graduate Scholarship (Declined), 2007
• Ontario Graduate Scholarship (Declined), 2007
• Ontario Graduate Scholarship in Science & Technology, 2006-2007
• NSERC Undergraduate Student Research Award, 2003-2005
• René Descartes National Scholarship, University of Waterloo, 2001-2006
• Harry Jerome National Scholarship, 2001-2005
• Canadian Millennium Scholarship, 2001-2002
Talks & Presentations
• Strong Nonnegativity & Sums of Squares on Real Varieties
– Algebra, Number Theory, Combinatorics Seminar, Claremont Colleges. Claremont,
California, Dec 2011.
– SIAM Conference on Applied Algebraic Geometry, North Carolina State University.
Raleigh, North Carolina, Oct 2011.
– AMS Special Session on Computational and Algorithmic Algebraic Geometry. Salt
Lake City, Utah, Oct 2011.
• On Volumes of Permutation Polytopes
– Combinatorics Seminar, Caltech. Pasadena, California, Sept 2011.
– AMS Special Session on Convexity & Combinatorics. Richmond, Virginia, Nov 2010.
– Math Department Seminar, Simon Fraser University, Burnaby Campus. Burnaby,
British Columbia, Oct 2010.
• Iterative Algebraic Algorithms for the Recognition of Combinatorial Properties
– Math Department Seminar, Simon Fraser University, Surrey Campus. Surrey, British
Columbia, Oct 2010.
– Research Group Seminar (Thorsten Theobald), Goethe-Universität Institut fur
Mathematik. Frankfurt, Germany, Nov 2009.
– Research Group Seminar (Michael Joswig), Technische Universität Darmstadt.
Darmstadt, Germany, Nov 2009.
– Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM 2009).
Montreal, Quebec, Canada, May 2009.
Service
• Siemens Competition, Judge, 2012.
• Caltech SURF (Summer Undergraduate Research) Presentation Day, Session Chair, 2012.
• Caltech Combinatorics Seminar, Organizer, 2011-2012.
• Caltech Postdoc Association, Event Program Chair, 2012.
• Caltech Postdoc Association, Executive Secretary, 2011-2012.
• Advisory Panel Member, American Mathematics Competition, 2011 - present.
• AMS-MAA Joint Math Meetings Undergraduate Poster Session Judge, 2011.
• Galois Group Tutoring Fundraiser Organizer, 2010.
• UC Davis Student Run Discrete Math Seminar Organizer, 2010.
• Competition Writer, Mathleague.org Competitions, 2009-present.
• UC Davis Graduate Program Committee Representative, 2009.
• UC Davis Undergraduate Research Mentor, 2009.
• Oakland/East Bay Math Circle Guest Lecture, 2008.
• American Mathematics Society Graduate Student Blog Editorial Board, 2008.
• UC Davis Graduate Student Association Representative, 2008.
• Competition Grader, Canadian Mathematics Competitions, 2002-2007.
• Refereed Articles for Journal of Combinatorial Designs, Journal of Integer Sequences,
Discrete Optimization.
Skills
• Math Programming: 4ti2, Java, Latte, Macaulay 2, Maple, Matlab, Python, Sage
• Languages: English, some Arabic, some French.