Research Groups

Algebra

Lowell Abrams, Low Dimensional Combinatorial Topology,Topological Graph Theory, Combinatorial Algebra

Analysis

John Conway (Emeritus), Function theoretic operator, Non-abelian approximation
Maria Gualdani, Nonlinear Partial Differential Equations of Diffusion Type, Existence and Qualitative Analysis, Entropy Methods, Rate of Convergence to Equilibrium, Mean Field Games
Hugo D. Junghenn, Functional Analysis, Semigroups, Financial Math
E.Arthur Robinson, Ergodic Theory, Functional Analysis, Aperiodic Order, Computational Math
Svetlana Roudenko, Nonlinear Dispersive PDEs, Harmonic Analysis, Signal and Image Analysis, Medical Imaging

Applied Mathematics

Frank E. Baginski, Applied Mathematics, Partial Differential Equations
Maria Gualdani, Nonlinear Partial Differential Equations of Diffusion Type, Existence and Qualitative Analysis, Entropy Methods, Rate of Convergence to Equilibrium, Mean Field Games
Murli M. Gupta, Numerical Analysis, Computational Fluid Dynamics, Mathematical Education
Chunlei Liang, Computational Fluid Dynamics, Astrophysics, Tidal/Wind Energy, Fluid-Structure Interaction, Biomechanics
Xiaofeng Ren, Partial Differential Equations, Applied Mathematics
Svetlana Roudenko, Nonlinear Dispersive PDEs, Harmonic Analysis, Signal and Image Analysis, Medical Imaging
Yanxiang Zhao, Numerical Analysis, Numerical Methods for differential equations

Combinatorics and Graph Theory

Joseph E. Bonin, Combinatorics, Matroid Theory
Daniel Ullman, Graph Theory, Combinatorics

Computational Biology

Max Alekseyev,  Computational Molecular Biology/Bioinformatics, Comparative Genomics, Graph Theory, Combinatorics, Discrete Algorithms
Yongwu Rong, Topology, Low Dimensional Manifolds
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
Yongwu Rong, Topology, Low Dimensional Manifolds
Alexander Shumakovitch, Low-Dimensional Topology, Knot Theory
Hao Wu, Geometric Topology, Especially 3-dimensional Contact Topology, Heegaard-Floer Theory and Khovanov-Rozansky Theory

 

Funding

NSF

  • 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, Harizanov, Valentina
  • 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 Phenomina in Evloution 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.
     

NASA

  • 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.


NSA

  • 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
     

UFF/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

Other

  • Algebraic structures motivated by and applied to Knot Theory, Simons Fundation, granted for 5 years, 2014-2019, Jozef Przytyck.
  • Khovanov Homology Theories and their Applications, 2013-2018, Simons Foundation, Shumakovitch, Alexander
  • MAA grant RUMC (Research Undergraduate Math Conference), joint conferences of DC-area universities, Roudenko(PI 2013), Rong(PI 2012)
  • Undergraduate Math Conferance, 2013, Mathematical Association of America, Roudenko, Svetlana
  • Dc FAME II 2011, DC Office of the State Superintendent of Education, Ullman, Daniel H.
  • Geometric Structures in Self Organizing Physical and Biological Systems, Simons Foundation, Ren, Xiaofeng
  • Dynamical Systems and Aperiodic Orderopics in Global Behavior of Soluations 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
  • 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.

Centers & Institutes

Center for Quantum Computing, Information, Logic & Topology

The George Washington University's Center for Quantum Computing, Information, Logic, and Topology is a multi-disciplinary initiative bringing cutting-edge science and mathematics to GW. The primary mission of the Center is to add synergistic coherence to GW contributions toward advancing the subject of quantum computing. By promoting scholarship, collaboration, and dissemination via research volumes and articles, seminars, workshops and high profile conferences at GW, the Center provides leadership for the Washington area in the potentially transformative quantum computation and information theory. 

Institute for Mathematical Sciences

The purpose of the Institute is to link research and training opportunities in cutting-edge applications of mathematical sciences to areas with emerging needs for  mathematics. To serve as a hub for researchers with different backgrounds to communicate with each other on their work, to explore collaboration opportunities on inter-disciplinary research and training, to connect GW with outside leaders, and to increase the reputation of GW as a national research center in our capital. 

Director: Yongwu Rong, gwims@gwu.edu