## 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 Theor**y**

## 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