NSERC Discovery Grant
2025–2030 · National Research Grant
York University · Toronto
Mohamed
Omar
Professor, Department of Mathematics & Statistics, York University
About
Academic profile
Welcome to my academic page! I am a professor in the Department of Mathematics and Statistics at York University in my hometown of Toronto, Ontario, Canada. Previously I spent a decade as an associate and assistant professor in the Department of Mathematics at Harvey Mudd College. I completed my postdoctoral fellowship in the Department of Mathematics at Caltech. My PhD was completed in the Department of Mathematics at UC Davis under the advising of Jesús De Loera.
I am currently very research active and accepting invitations for collaborative workshops, conferences to meet collaborators and spark new projects, and research meetings.
However, I am currently on hiatus from giving any public talks, research or seminar talks, colloquia, or plenary talks.
Recognition
Recent Awards and Grants
AMS Claytor-Gilmer Fellowship
Inaugural · National Research Award
Karen EDGE Fellowship
Inaugural · National Research Award
Henry L. Alder Award
National Teaching Award
Research archive
Journal Articles
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Submitted
Multiple Distance Ramsey Bounds For Graphs in Euclidean Spaces
submitted, 21 pp. w/ Ayşegül Kula Jonah Stockwell, Mckinley Xie
Develops lower bounds in Euclidean Ramsey Theory problems that are natural extensions of the Hadwiger-Nelson problem.
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Submitted
Ehrhart Theory over Abelian Groups
submitted, 22 pp. w/ Robert Davis, Jesús A. De Loera, Alexey Garber, Katharina Jochemko, Josephine Yu
Develops an Ehrhart-theoretic framework over abelian groups and studies the counting functions and structural phenomena that arise in that setting.
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Shows that real roots of reliability polynomials of simple graphs form a dense set, extending the known landscape of graph reliability roots.
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Develops new methods for studying coefficient unimodality in domination polynomials and obtains improved sufficient conditions for unimodality.
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Studies permutations with a prescribed X-descent set, deriving enumerative formulas and structural results for the associated permutation classes.
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To appear
On a Quadratic Relation Between Stanley-Wilf Limits and Füredi-Hajnal Limits
to appear, Discrete Mathematics Letters, 5 pp.
Establishes a quadratic relationship between Stanley-Wilf limits and Füredi-Hajnal limits for permutation patterns.
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2026
Growth Rates of Permutations with Given Descent or Peak Set
European Journal of Combinatorics, 131, 104246, 2026. — w/ Justin Troyka
Determines growth rates for permutations constrained by a given descent or peak set and relates the two families.
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2025
Revisiting Rédei Berge Symmetric Functions via Matrix Algebra
Electronic Journal of Combinatorics, Vol 32(4), P.4.43, 2025. — w/ John Irving
Recasts Rédei-Berge symmetric functions through matrix algebra, yielding new formulas, interpretations, and proofs.
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Connects partition rank decompositions with the combinatorics of partition lattices and develops rank bounds from that relationship.
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2023
Sets Avoiding Full-Rank Three-Point Patterns in (Fqn)k Are Exponentially Small
Australasian Journal of Combinatorics, 85(3): 423-429, 2023.
Proves exponential upper bounds for subsets of finite-field spaces that avoid prescribed full-rank three-point configurations.
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Investigates graph burning across graph classes, identifying structural conditions and bounds for the burning number.
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2022
On Distinct Distances Between a Variety and a Point Set
Electronic Journal of Combinatorics, 29(3), P3.21, 2022. — w/ Bryce McLaughlin
Gives bounds for the number of distinct distances determined between a fixed algebraic variety and a finite point set.
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2022
Factorization Length Distribution For Affine Semigroups III: Modular Equidistribution for Numerical Semigroups with Arbitrarily Many Generators
Journal of the Australian Mathematical Society, 113(1): 21-35, 2022. — w/ Stephan Ramon Garcia, Christopher O'Neill, Timothy Wesley
Proves modular equidistribution results for factorization lengths in numerical semigroups with arbitrarily many generators.
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2021
Factorization Length Distribution For Affine Semigroups II: Asymptotic Behavior for Numerical Semigroups with Arbitrarily Many Generators
Journal of Combinatorial Theory, Series A, 178: 105358, 2021. — w/ Stephan Ramon Garcia, Christopher O'Neill, Samuel Yih
Determines the asymptotic distribution of factorization lengths in numerical semigroups with arbitrarily many generators.
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2021
Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
Linear Algebra and its Applications, 608: 68-83, 2021. — w/ Albrecht Böttcher, Stephan Ramon Garcia, Christopher O'Neill
Relates weighted means of B-splines, positivity of divided differences, and complete homogeneous symmetric polynomials through a common algebraic framework.
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2019
Counting Peaks on Graphs
Australasian Journal of Combinatorics, 75(2): 174-189, 2019. — w/ Alex Diaz-Lopez, Lucas Everham, Pamela E. Harris, Erik Insko, Vince Marcantonio
Introduces and enumerates peak sets on graphs, extending classical permutation peak statistics to graph-labelled settings.
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2019
Descent Polynomials
Discrete Mathematics, 342: 1674-1686, 2019. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko, Bruce Sagan
Studies descent polynomials associated with prescribed descent sets, including their coefficients, roots, and positivity properties.
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2019
Sparse Neural Codes and Convexity
Involve, 12(5): 737-754, 2019. — w/ R. Amzi Jeffs, Natchanon Suaysom, Aleina Wachtel, Nora Youngs
Examines convex realizations of sparse neural codes and gives structural conditions governing convexity.
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Studies visibility of lattice points lying on power functions and derives asymptotic counting results.
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2018
Homomorphisms Preserving Neural Ideals
Journal of Pure and Applied Algebra, 222(11): 3470-3482, 2018. — w/ R. Amzi Jeffs, Nora Youngs
Characterizes homomorphisms that preserve neural ideals and describes their combinatorial effect on neural codes.
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2018
The q-analog of Kostant's partition function and the highest root of the classical Lie algebras
Australasian Journal Of Combinatorics, 71(1): 68-91, 2018. — w/ Pamela E. Harris, Erik Insko
Analyzes the q-analog of Kostant’s partition function for highest roots in the classical Lie algebras.
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2017
A Proof of the Peak Polynomial Positivity Conjecture
Journal of Combinatorial Theory Series A, 149: 21-29, 2017. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
Proves the peak polynomial positivity conjecture by establishing positivity for the relevant polynomial coefficients.
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2017
What makes a neural code convex?
SIAM Journal on Applied Algebra and Geometry, 1(1): 222-238, 2017. — w/ Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs
Identifies combinatorial and geometric conditions that determine when a neural code admits a convex realization.
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2016
Low Degree Nullstellensatz Certificates for 3-Colorability
Electronic Journal of Combinatorics, 23(1): P1.6, 2016. — w/ Bo Li, Benjamin Lowenstein
Constructs and bounds low-degree Nullstellensatz certificates for graph 3-colorability.
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2014
Chromatic Bounds on Orbital Chromatic Roots
Electronic Journal of Combinatorics, 21(4): P4.17, 2014. — w/ Dae Hyun Kim, Alexander H. Mun
Uses chromatic information to bound the roots of orbital chromatic polynomials.
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2013
Strong Nonnegativity and Sums of Squares on Real Varieties
Journal of Pure and Applied Algebra, 217(5): 843-850, 2013. — w/ Brian Osserman
Develops strong nonnegativity on real varieties and relates it to representations as sums of squares.
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2013
On Volumes of Permutation Polytopes
Fields Institute Communications, Discrete Geometry and Optimization, 55-77, 2013. — w/ Katherine Burggraf, Jesus De Loera
Studies volumes of permutation polytopes and derives formulas and bounds from the combinatorics of permutation groups.
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2012
On The Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9(6): 1843-1846, 2012. — w/ Christina Boucher
Establishes computational hardness results for counting and sampling center strings in biological sequence analysis.
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2010
Recognizing Graph Theoretic Properties with Polynomial Ideals
Electronic Journal of Combinatorics, 17(1): R114, 2010. — w/ Christopher Hillar, Jesus De Loera, Peter N. Malkin
Uses polynomial ideals and algebraic certificates to recognize graph-theoretic properties.
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2006
Asymptotics of Largest Components in Combinatorial Structures
Algorithmica, 46(3-4): 493-503, 2006. — w/ Daniel Panario, Bruce Richmond, Jacki Whitely
Derives asymptotic laws for the largest components in broad classes of combinatorial structures.
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Proceedings
Conference Articles
- 2018
New Perspectives on Flexibility in Simple Temporal Planning
ICAPS 2018, 18 pp., 2018. — w/ Jim Boerkoel, Amy Huang, Liam Lloyd
- 2017
A Proof of the Peak Polynomial Positivity Conjecture
FPSAC 2017, 10 pp., 2017. — w/ Alex Diaz-Lopez, Pamela E. Harris, Erik Insko
- 2010
On The Hardness of Counting and Sampling Center Strings
SPIRE 2010, 128-135, 2010. — w/ Christina Boucher
- 2008
Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers
DMTCS / 5th Colloquium on Math & CS, 195-206, 2008. — w/ Christopher Eagle, Zhicheng Gao, Daniel Panario, Bruce Richmond
Long-form work
Books
- 2021
Graph Theory You Need Before Undergrad Research: in 8 undergrad lectures
Amazon CreateSpace, 2021.
- 2017
Number Theory Toward RSA Cryptography: in 10 undergraduate lectures
Amazon CreateSpace, 2017.
- 2026
Putnam Prep Materials
(unpublished, reference only)
Theses
- Ph.D.
Applications of Convex and Algebraic Geometry to Graphs and Polytopes
Ph.D. Thesis. Advisor: Jesús De Loera. UC Davis, 2011.
- M.Math.
Combinatorial Approaches to the Jacobian Conjecture
Master’s Thesis. Advisor: Ian P. Goulden. University of Waterloo, 2007.