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 well-published 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

William Schmitt: Algebraic combinatorics, Hopf Algebras, Category Theory
Robert Won: Noncommutative Algebra, Quantum Symmetries, Weak Hopf Algebras

Hugo D. Junghenn: Functional Analysis, Semigroups, Financial Math
Lien-Yung (Nyima) Kao: Dynamic Systems, Thermodynamic Formalism, Ergodic Geometry

Frank E. Baginski: Applied Mathematics, Partial Differential Equations
Xiaofeng Ren: Partial Differential Equations, Applied Mathematics
Yanxiang Zhao: Numerical Analysis, Numerical Methods for differential equations

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

Max Alekseyev: Computational Molecular Biology/Bioinformatics, Comparative Genomics, Graph Theory, Combinatorics, Discrete Algorithms
Yanxiang Zhao: Numerical Analysis, Numerical Methods for differential equations

Valentina S. Harizanov: Logic, Recursion Theory, Recursive Model Theory
Michael Moses: Logic, Recursive Model Theory, Computational Complexity

Jozef H. Przytycki: Topology, Knot Theory, Algebraic Topology based on knots
Hao Wu: Geometric Topology, Especially 3-dimensional Contact Topology, Heegaard-Floer Theory, Khovanov-Rozansky Theory

Faculty Grant Funding

National Science Foundation

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).
EXTREEMS-QED: GW Mathematics and Statistics Training, Education, & Research (MASTER), 2014-2018, Yongwu Rong (PI), Maria Gualdani, Murli Gupta, Yinglei Lai, and Rahul Simha (Co-PI).
Analysis of nonlocal effects in nonlinear parabolic partial differential equations, 2014-2017, Maria Gualdani.
Building Capacity for Disciplinary Experts in Math and Science Teaching, 2014-2015, PI: Curtis Pyke, Co-PI: Daniel Ullman, Larry Medsker, Hartmut G. Doebel.
Multi-Constituent inhibitory systems with self-organizing properties, 2013-2016, Ren, Xiaofeng
WIDER: Planning: GW Reform and Advancement of STEM-education Practices (GRASP), 2013-2018, PI: Rahul Simha, Yongwu Rong (Co-PI).
Jump: Joint Undergraduate Mathematics and Physics Scholarships at GW 2013-2018, Rong, Yongwu.
JUMP: Joint Undergraduate Mathematics and Physics Scholarships at GW, Y. Rong(PI), D. Ulmann(co-PI), L. Medsker(co-PI, Physics), G. Fieldman(co-PI, Physics), S. Roudenko(co-PI); 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, 2011-2014, DMS-1137422 Jozef Przytycki (PI), Valentina Harizanov (Co-PI), Alexander Shumakovitch (Co-PI), Hao Wu (Co-PI), 9/1/11-8/31/14.
Dispersive PDE CAREER: Nonlinear Phenomena in Evolution PDE, Roudenko, Svetlana.
Topics in Global Behavior of Solutions to nonlinear dispersive PDE, DMS-1103274, Svetlana Roudenko (PI), 9/1/11-8/31/14.
Singular limits, saturation, and defects in block copolymer morphology , DMS-0907777, Xiaofeng Ren (PI), 7/1/09-6/30/12.
Topics in Computable Mathematics, DMS-0904101, Valentina Harizanov (PI), 7/1/09-6/30/12.
Knots in Poland III; the conference on Knot Theory and its Ramifications, DMS-1034753, Jozef Przytycki (PI), Mikhail Khovanov (Co-PI), 7/1/10-6/30/11.
Knots in Washington: Conferences on Knot Theory and its Ramifications 2008-2010, DMS-0817858, Jozef Przytycki (PI), Alexander Shumakovitch (Co-PI), Hao Wu (Co-PI), Yongwu Rong (Co-PI), 5/15/08-4/30/11.
CDI-type II: Understanding Complex Biological Networks: A Process Viewpoint, Chen Zeng (PI), Yongwu Rong, Rahul Simha (CO-PI), NSF, Cyber-enabled Discovery and Innovation (CDI) program, CMMI-0941228, 2009 – 2013.

National Aeronautics and Space Administration

ExaVolt Antenna: Supporting Technology for Suborbital Ultra-high Energy Particle Accelerators, George Washington University, NASA Goddard Space Flight Center, Frank E Baginski, 01/10/2012 - 01/09/2015.

National Security Agency

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

GW University Facilitating Fund (UFF) and Columbian College Facilitating Fund (CCFF)

Singularity Formation in Evolution Equations and Pedagogical Connections of Math, Biology and Medical Imaging, Svetlana Roudenko
Quantum Computations, Complexity and Information, V. Harizanov (PI) co-PIs: A. Eskandarian, (Physics), W. Parke (Physics) and J. Przytycki (Mathematics)
Properties and Applications of Link Homology Theories, Alexander Shumakovitch
Combinatorial link homologies and 3-manifold invariants, Hao Wu

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Simons Foundation

Joel Brewster Lewis, " Permutations, reflection groups, and factorization combinatorics", Simons Foundation Collaboration Grants for Mathematicians (grant 634530), 2019-2024
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 Sciences-Collaboration Grants for Mathematicians. Project Title: Thermodynamic formalism, deformation theory, and non-uniformly hyperbolic dynamics in geometry. Award Number: 956047 Period: Sep 2022— Aug 2026; Kao, Lien-Yung.
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, 2014-2019, 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

Other

Joel Brewster Lewis, "Combinatorics of Reflection Groups", ORAU Powe Junior Faculty Enhancement Award, 2019-2020
MAA grant RUMC (Research Undergraduate Math Conference), joint conferences of DC-area 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), 2010-12
Collaboration in Computability, NSF research bi-national (with Russia/Kazakhstan) grant DMS-1101123, 5/1/011-4/30/2014, J. Knight (PI), V. Harizanov (senior personnel).
Nonlinear Dispersive PDE, Simons Foundation, Roudenko Svetlana
Polish Scientific Grant: Nr. N N201387034; Jozef Przytycki (Co-PI), 4/29/08-4/29/11.