Research
Research in the GW Department of Mathematics explores topics within the core focus areas of algebra, analysis, applied mathematics, combinatorics and graph theory, computational biology, logic and topology. Our wellpublished faculty regularly secure grant funding from institutions such as the National Science Foundation, the National Security Agency and NASA.
Undergraduate mathematics students earn a range of departmental prizes and academic honors in recognition of their research, and graduate students learn to conduct sophisticated, scholarly research suitable for publication during their degree programs.
Faculty by Core Research Area
Algebra
 William Schmitt: Algebraic combinatorics, Hopf Algebras, Category Theory
 Robert Won: Noncommutative Algebra, Quantum Symmetries, Weak Hopf Algebras
Analysis
 John Conway (Emeritus): Function theoretic operator, Nonabelian approximation
 Hugo D. Junghenn: Functional Analysis, Semigroups, Financial Math
 E. Arthur Robinson: Ergodic Theory, Functional Analysis, Aperiodic Order, Computational Math
 LienYung (Nyima) Kao: Dynamic Systems, Thermodynamic Formalism, Ergodic Geometry
Applied Mathematics
 Frank E. Baginski: Applied Mathematics, Partial Differential Equations
 Murli M. Gupta: Numerical Analysis, Computational Fluid Dynamics, Mathematical Education
 Xiaofeng Ren: Partial Differential Equations, Applied Mathematics
 Yanxiang Zhao: Numerical Analysis, Numerical Methods for differential equations
Combinatorics and Graph Theory
 Joseph E. Bonin: Combinatorics, Matroid Theory
 Daniel Ullman: Graph Theory, Combinatorics
 Joel B. Lewis: Enumerative and Algebraic Combinatorics
 William Schmitt: Algebraic combinatorics, Hopf Algebras, Category Theory
Computational Biology
 Max Alekseyev: Computational Molecular Biology/Bioinformatics, Comparative Genomics, Graph Theory, Combinatorics, Discrete Algorithms
 Yanxiang Zhao: Numerical Analysis, Numerical Methods for differential equations
Logic
 Valentina S. Harizanov: Logic, Recursion Theory, Recursive Model Theory
 Michael Moses: Logic, Recursive Model Theory, Computational Complexity
Topology
 Lowell Abrams: Low Dimensional Combinatorial Topology,Topological Graph Theory, Combinatorial Algebra
 Jozef H. Przytycki: Topology, Knot Theory, Algebraic Topology based on knots
 Hao Wu: Geometric Topology, Especially 3dimensional Contact Topology, HeegaardFloer Theory, KhovanovRozansky Theory
Faculty Grant Funding

FRG: Collaborative Research: Definability and Computability over Arithmetically Significant Fields for 3 years starting July 15, 2022. Valentina Harizanov (PI).
 Reconstruct morphological phases from nonlocal geometric systems, August 15, 2017  July 31, 2020, Xiaofeng Ren (PI).
 EXTREEMSQED: GW Mathematics and Statistics Training, Education, & Research (MASTER), 20142018, Yongwu Rong (PI), Maria Gualdani, Murli Gupta, Yinglei Lai, and Rahul Simha (CoPI).

Analysis of nonlocal effects in nonlinear parabolic partial differential equations, 20142017, Maria Gualdani.
 Building Capacity for Disciplinary Experts in Math and Science Teaching, 20142015, PI: Curtis Pyke, CoPI: Daniel Ullman, Larry Medsker, Hartmut G. Doebel.
 MultiConstituent inhibitory systems with selforganizing properties, 20132016, Ren, Xiaofeng
 WIDER: Planning: GW Reform and Advancement of STEMeducation Practices (GRASP), 20132018, PI: Rahul Simha, Yongwu Rong (CoPI).
 Jump: Joint Undergraduate Mathematics and Physics Scholarships at GW 20132018, Rong, Yongwu.
 JUMP: Joint Undergraduate Mathematics and Physics Scholarships at GW, Y. Rong(PI), D. Ulmann(coPI), L. Medsker(coPI, Physics), G. Fieldman(coPI, Physics), S. Roudenko(coPI); 8/1/13 7/31/16.
 Combinatorial Link Homologies and Their Applications, Wu, Hao

Topics in Computable Structure Theory, DMS 1202328, Valentina Harizanov (PI), 7/1/2012–6/30/2016
 Topics in Computable Mathematics, Harizanov, Valentina.
 Knots in Washington: Conferences on Knot Theory and its Ramifications, including Quantum Computing, 20112014, DMS1137422 Jozef Przytycki (PI), Valentina Harizanov (CoPI), Alexander Shumakovitch (CoPI), Hao Wu (CoPI), 9/1/118/31/14.
 Dispersive PDE CAREER: Nonlinear Phenomena in Evolution PDE, Roudenko, Svetlana.
 Topics in Global Behavior of Solutions to nonlinear dispersive PDE, DMS1103274, Svetlana Roudenko (PI), 9/1/118/31/14.
 Singular limits, saturation, and defects in block copolymer morphology , DMS0907777, Xiaofeng Ren (PI), 7/1/096/30/12.
 Topics in Computable Mathematics, DMS0904101, Valentina Harizanov (PI), 7/1/096/30/12.
 Knots in Poland III; the conference on Knot Theory and its Ramifications, DMS1034753, Jozef Przytycki (PI), Mikhail Khovanov (CoPI), 7/1/106/30/11.
 Knots in Washington: Conferences on Knot Theory and its Ramifications 20082010, DMS0817858, Jozef Przytycki (PI), Alexander Shumakovitch (CoPI), Hao Wu (CoPI), Yongwu Rong (CoPI), 5/15/084/30/11.
 CDItype II: Understanding Complex Biological Networks: A Process Viewpoint, Chen Zeng (PI), Yongwu Rong, Rahul Simha (COPI), NSF, Cyberenabled Discovery and Innovation (CDI) program, CMMI0941228, 2009 – 2013.
 ExaVolt Antenna: Supporting Technology for Suborbital Ultrahigh Energy Particle Accelerators, George Washington University, NASA Goddard Space Flight Center, Frank E Baginski, 01/10/2012  01/09/2015.
 Summer Program for Women in Mathematics, Murli M. Gupta
 Investigating Algebraic Structures Motivated by Knot Theory: homology of quandles, Burnside groups, skein modules and Khovanov homology, Jozef Przytycki
 Structure of Combinatorial Hopf algebras, William R. Schmitt
 Singularity Formation in Evolution Equations and Pedagogical Connections of Math, Biology and Medical Imaging, Svetlana Roudenko
 Quantum Computations, Complexity and Information, V. Harizanov (PI) coPIs: A. Eskandarian, (Physics), W. Parke (Physics) and J. Przytycki (Mathematics)
 Properties and Applications of Link Homology Theories, Alexander Shumakovitch
 Combinatorial link homologies and 3manifold invariants, Hao Wu
 Joel Brewster Lewis, " Permutations, reflection groups, and factorization combinatorics", Simons Foundation Collaboration Grants for Mathematicians (grant 634530), 20192024
 Topics in Computable Structure Theory, Simons Foundation, # 853762, period 9/2021– 8/2026, Valentina Harizanov.

Computability in Algebraic Structures, Simons Foundation, #429466, period 9/2016 – 8/2022, Valentina Harizanov.

Simons Foundation, Program: Mathematics and Physical SciencesCollaboration Grants for Mathematicians. Project Title: Thermodynamic formalism, deformation theory, and nonuniformly hyperbolic dynamics in geometry. Award Number: 956047 Period: Sep 2022— Aug 2026; Kao, LienYung.

Simons personal grant (PI): granted for 5 years, September 1, 2019 August 31, 2024. Award Number: ECNS21687N ( 637794). Project Title: In search for connections between Khovanov and Yang Baxter homologies. Total amount: $42,000.00. Jozef H. Przytycki.
 Simons Foundation, Collaboration Grant for Mathematicians, Geometric variational problems and elliptic functions, September 1, 2020  August 31, 2025, Xiaofeng Ren (PI).
 Algebraic structures motivated by and applied to Knot Theory, Simons Foundation, granted for 5 years, 20142019, Jozef Przytyck.
 Geometric Structures in Self Organizing Physical and Biological Systems, Simons Foundation, Ren, Xiaofeng
 Dynamical Systems and Aperiodic Orderopics in Global Behavior of Solutions to Nonlinear, Simons Foundation, Robinson, E. Arthur
 Studies in Global Behavior of Solutions in Nonlinear Dispersive PDE, Simons Foundation, Roudenko, Svetlana
 Link Homologies and Their Applications, Simons Foundation, Wu, Hao
 Joel Brewster Lewis, "Combinatorics of Reflection Groups", ORAU Powe Junior Faculty Enhancement Award, 20192020
 MAA grant RUMC (Research Undergraduate Math Conference), joint conferences of DCarea universities, Roudenko(PI 2013), Rong(PI 2012)
 Undergraduate Math Conference, 2013, Mathematical Association of America, Roudenko, Svetlana
 Dc FAME II 2011, DC Office of the State Superintendent of Education, Ullman, Daniel H.
 District of Columbia Fellows Advancing Mathematics Education (DC FAME), DC Gov, Daniel Ullman (PI), 201012
 Collaboration in Computability, NSF research binational (with Russia/Kazakhstan) grant DMS1101123, 5/1/0114/30/2014, J. Knight (PI), V. Harizanov (senior personnel).
 Nonlinear Dispersive PDE, Simons Foundation, Roudenko Svetlana
 Polish Scientific Grant: Nr. N N201387034; Jozef Przytycki (CoPI), 4/29/084/29/11.
Spotlight on Student Research
Computer Science for Social Good
Samsara Counts, a senior majoring in computer science and mathematics, used deep learning methods to develop tools that help patients with eating disorders avoid triggering images online.
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