Thomas Wanner
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, Virginia 22030, USA

 

Curriculum Vitae

Education

  • 1993 Dr.rer.nat. (Ph.D.), Universität Augsburg (Germany), Mathematics
  • 1991 Diplom (M.S.), Universität Augsburg, Mathematics, Computer Science
  • 1989 Vordiplom (B.S.), Universität Augsburg, Mathematics, Computer Science

Experience in Higher Education

  • 2011– George Mason University, Professor
  • 2004–2011 George Mason University, Associate Professor
  • 2002–2004 George Mason University, Assistant Professor
  • 2002–2004 University of Maryland, Baltimore County, Adjunct Assistant Professor
  • 1998–2002 University of Maryland, Baltimore County, Assistant Professor
  • 1997–1998 Universität Augsburg, Assistant Professor
  • 1996–1997 Georgia Institute of Technology, Visiting Assistant Professor
  • 1995–1996 Georgia Institute of Technology, Visiting Research Scholar
  • 1993–1995 Universität Augsburg, Postdoctoral Fellow
  • 1989–1993 Universität Augsburg, Teaching Assistant

Visiting Appointments

  • Summer 2022 International Centre for Mathematical Sciences, Edinburgh, Scotland
  • Fall 2017 Hausdorff Research Institute for Mathematics, Bonn, Germany
  • Spring 2014 Institute for Mathematics and its Applications, Minneapolis, Minnesota
  • Fall 2012 Institute for Mathematics and its Applications, Minneapolis, Minnesota
  • Summer 2010 Isaac Newton Institute, Cambridge, United Kingdom
  • Fall 2006 Mathematical Sciences Research Institute, Berkeley, California

External Research Support

  • 2025–2030 Simons Foundation Grant (SFI-MPS-TSM-00013686, $37,100, PI), Verified and combinatorial topological dynamics
  • 2018–2025 Simons Foundation Collaboration Grant (Award 581334, $42,000, PI), Topological methods in dynamical systems
  • 2014–2018 National Science Foundation Grant (DMS-1407087, $599,885, co-PI), EXTREEMS-QED: Undergraduate research in computational and data-enabled mathematics
  • 2011–2015 National Science Foundation Grant (DMS-1114923, $180,000, PI), Probabilistic methods in computational topology
  • 2009–2013 National Science Foundation Grant (DMS-0907818, $105,000, PI), A hybrid of theoretical and computational methods for bifurcation analysis
  • 2006–2012 National Science Foundation Grant (DMS-0639300, $1,057,257, co-PI), CSUMS: Development of an ongoing program of undergraduate computational mathematics research
  • 2005–2010 U.S. Department of Energy Grant (DOE-97889, $297,833, PI), Multiscale analysis of nonlinear systems using computational homology
  • 2004–2009 National Science Foundation Grant (DMS-0406231, $100,002, PI), Complex transient patterns in phase-field models

Other Research Support and Fellowships

  • 2014 Faculty Study Leave, GMU
  • 2004 Provost’s Tenure-Track Assistant Professor Leave, Spring Semester, GMU
  • 2003 Provost’s Award for Summer Research Funding, GMU
  • 2001 Summer Support, DOE Grant (Curtis Menyuk, UMBC)
  • 2000–2001 DRIF-RAS Grant, UMBC
  • 1999 Summer Faculty Fellowship, UMBC
  • 1996–1997 Research Fellowship Wa 960/3-2, Deutsche Forschungsgemeinschaft
  • 1995–1996 Research Fellowship Wa 960/3-1, Deutsche Forschungsgemeinschaft
  • 1991–1993 Ph.D. Fellowship, Deutsche Forschungsgemeinschaft
  • 1989–1991 Fellowship of the Studienstiftung des deutschen Volkes

Publications

Books

  1. ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes. Julia Package Manual, GitHub, v0.7.16, 275 pages, 2025.
  2. Connection Matrices in Combinatorial Topological Dynamics (with Marian Mrozek). SpringerBriefs in Mathematics, Springer, Cham, 165 pages, 2025.

Articles in refereed journals

  1. Conley index for multivalued maps on finite topological spaces (with Jonathan Barmak, Marian Mrozek). Foundations of Computational Mathematics 26(2), pp. 647–687, 2026.
  2. ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes. Journal of Open Source Software 10(111), Paper No. 8085, 5 pp, 2025.
  3. Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model (with Peter Rizzi, Evelyn Sander). Discrete and Continuous Dynamical Systems, Series B 29(2), pp. 666–701, 2024.
  4. Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces (with Michal Lipinski, Jacek Kubica, Marian Mrozek). Journal of Applied and Computational Topology 7(2), pp. 139–184, 2023.
  5. A computer-assisted study of red coral population dynamics (with Sayomi Kamimoto, Hye Kyung Kim, Evelyn Sander). Pure and Applied Functional Analysis 7(4), pp. 1307–1337, 2022.
  6. Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators (with Peter Rizzi, Evelyn Sander). Communications in Nonlinear Science and Numerical Simulation 115, Paper No. 106789, 27 pp, 2022.
  7. Combinatorial vs. classical dynamics: Recurrence (with Marian Mrozek, Roman Srzednicki, Justin Thorpe). Communications in Nonlinear Science and Numerical Simulation 108, Paper No. 106226, 30 pp, 2022.
  8. Creating semiflows on simplicial complexes from combinatorial vector fields (with Marian Mrozek). Journal of Differential Equations 304, pp. 375–434, 2021.
  9. Equilibrium validation in models for pattern formation based on Sobolev embeddings (with Evelyn Sander). Discrete and Continuous Dynamical Systems, Series B 26(1), pp. 603–632, 2021.
  10. Linking combinatorial and classical dynamics: Conley index and Morse decompositions (with Bogdan Batko, Tomasz Kaczynski, Marian Mrozek). Foundations of Computational Mathematics 20(5), pp. 967–1012, 2020.
  11. A Lefschetz fixed point theorem for multivalued maps of finite spaces (with Jonathan Barmak, Marian Mrozek). Mathematische Zeitschrift 294(3–4), pp. 1477–1497, 2020.
  12. Analyzing the squared distance-to-measure gradient flow system with k-order Voronoi diagrams (with Patrick O’Neil). Discrete & Computational Geometry 61(1), pp. 91–119, 2019.
  13. Validated bounds on embedding constants for Sobolev space Banach algebras. Mathematical Methods in the Applied Sciences 41(18), pp. 9361–9376, 2018.
  14. Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model (with Jacek Cyranka). SIAM Journal on Applied Dynamical Systems 17(1), pp. 694–731, 2018.
  15. Rigorous cubical approximation and persistent homology of continuous functions (with Pawel Dlotko). Computers and Mathematics with Applications 75(5), pp. 1648–1666, 2018.
  16. Rigorous continuation of bifurcation points in the diblock copolymer equation (with Jean-Philippe Lessard, Evelyn Sander). Journal of Computational Dynamics 4(1–2), pp. 71–118, 2017.
  17. Probabilistic estimates of the maximum norm of random Neumann Fourier series (with Dirk Blömker, Philipp Wacker). Communications in Nonlinear Science and Numerical Simulation 47, pp. 348–369, 2017.
  18. Computer-assisted equilibrium validation for the diblock copolymer model. Discrete and Continuous Dynamical Systems, Series A 37(2), pp. 1075–1107, 2017.
  19. Towards a formal tie between combinatorial and classical vector field dynamics (with Tomasz Kaczynski, Marian Mrozek). Journal of Computational Dynamics 3(1), pp. 17–50, 2016.
  20. Validated saddle-node bifurcations and applications to lattice dynamical systems (with Evelyn Sander). SIAM Journal on Applied Dynamical Systems 15(3), pp. 1690–1733, 2016.
  21. Topological microstructure analysis using persistence landscapes (with Pawel Dlotko). Physica D: Nonlinear Phenomena 334(1), pp. 60–81, 2016.
  22. Degenerate nucleation in the Cahn-Hilliard-Cook model (with Dirk Blömker, Evelyn Sander). SIAM Journal on Applied Dynamical Systems 15(1), pp. 459–494, 2016.
  23. Rigorous validation of isolating blocks for flows and their Conley indices (with Thomas Stephens). SIAM Journal on Applied Dynamical Systems 13(4), pp. 1847–1878, 2014.
  24. A randomized subdivision algorithm for determining the topology of nodal sets (with Gregory S. Cochran, Pawel Dlotko). SIAM Journal on Scientific Computing 35(5), pp. B1034–B1054, 2013.
  25. Branch interactions and long-term dynamics for the diblock copolymer model in one dimension (with Ian Johnson, Evelyn Sander). Discrete and Continuous Dynamical Systems, Series A 33(8), pp. 3671–3705, 2013.
  26. Coreduction homology algorithm for regular CW-complexes (with Pawel Dlotko, Tomasz Kaczynski, Marian Mrozek). Discrete & Computational Geometry 46(2), pp. 361–388, 2011.
  27. The dynamics of nucleation in stochastic Cahn-Morral systems (with Jonathan P. Desi, Hanein Edrees, Joseph J. Price, Evelyn Sander). SIAM Journal on Applied Dynamical Systems 10(2), pp. 707–743, 2011.
  28. Coreduction homology algorithm for inclusions and persistent homology (with Marian Mrozek). Computers and Mathematics with Applications 60(10), pp. 2812–2833, 2010.
  29. Topology-guided sampling of nonhomogeneous random processes (with Konstantin Mischaikow). Annals of Applied Probability 20(3), pp. 1068–1097, 2010.
  30. Nucleation in the one-dimensional stochastic Cahn-Hilliard model (with Dirk Blömker, Bernhard Gawron). Discrete and Continuous Dynamical Systems, Series A 27(1), pp. 25–52, 2010.
  31. Homology metrics for microstructure response fields in polycrystals (with Edwin R. Fuller, David M. Saylor). Acta Materialia 58(1), pp. 102–110, 2010.
  32. Verified homology computations for nodal domains (with Sarah Day, William D. Kalies). SIAM Journal on Multiscale Modeling & Simulation 7(4), pp. 1695–1726, 2009.
  33. A semi-implicit spectral method for stochastic nonlocal phase-field models (with Tina Hartley). Discrete and Continuous Dynamical Systems, Series A 25(2), pp. 399–429, 2009.
  34. Rigorous numerics for the Cahn-Hilliard equation on the unit square (with Stanislaus Maier-Paape, Ulrich Miller, Konstantin Mischaikow). Revista Matematica Complutense 21(2), pp. 351–426, 2008.
  35. Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation (with Dirk Blömker, Stanislaus Maier-Paape). Transactions of the American Mathematical Society 360(1), pp. 449–489, 2008.
  36. Probabilistic and numerical validation of homology computations for nodal domains (with Sarah Day, William D. Kalies, Konstantin Mischaikow). Electronic Research Announcements of the American Mathematical Society 13, pp. 60–73, 2007.
  37. Structure of the attractor of the Cahn-Hilliard equation on a square (with Stanislaus Maier-Paape, Konstantin Mischaikow). International Journal of Bifurcation and Chaos 17(4), pp. 1221–1263, 2007.
  38. A Hermite spectral method for the computation of homoclinic orbits and associated functionals (with Valeriy Korostyshevskiy). Journal of Computational and Applied Mathematics 206(2), pp. 986–1006, 2007.
  39. Probabilistic validation of homology computations for nodal domains (with Konstantin Mischaikow). Annals of Applied Probability, 17(3), pp. 980–1018, 2007.
  40. Complex transient patterns on the disk (with Jonathan P. Desi, Evelyn Sander). Discrete and Continuous Dynamical Systems, Series A, 15(4), pp. 1049–1078, 2006.
  41. Topological simplification of nonautonomous difference equations (with Bernd Aulbach). Journal of Difference Equations and Applications, 12(3-4), pp. 283–296, 2006.
  42. Evolution of pattern complexity in the Cahn-Hilliard theory of phase separation (with Marcio Gameiro, Konstantin Mischaikow). Acta Materialia, 53(3), pp. 693–704, 2005.
  43. Maximum norms of random sums and transient pattern formation. Transactions of the American Mathematical Society, 356(6), pp. 2251–2279, 2004.
  44. Polarization decorrelation in optical fibers with randomly varying elliptical birefringence (with Brian S. Marks, Curtis R. Menyuk, John Zweck). Optics Letters, 28(19), pp. 1799–1801, 2003.
  45. Pattern formation in a nonlinear model for animal coats (with Evelyn Sander). Journal of Differential Equations, 191(1), pp. 143–174, 2003.
  46. Invariant foliations and decoupling of non-autonomous difference equations (with Bernd Aulbach). Journal of Difference Equations and Applications, 9(5), pp. 459–472, 2003.
  47. Existence and uniqueness of risk-sensitive estimates (with James Lo). IEEE Transactions on Automatic Control, 47(11), pp. 1945–1948, 2002.
  48. Enstrophy dynamics of stochastically forced large-scale geophysical flows (with Dirk Blömker, Jinqiao Duan). Journal of Mathematical Physics, 43(5), pp. 2616–2626, 2002.
  49. Roughness in surface growth equations (with Dirk Blömker, Stanislaus Maier-Paape). Interfaces and Free Boundaries, 3(4), pp. 465–484, 2001.
  50. Spinodal decomposition for the Cahn-Hilliard-Cook equation (with Dirk Blömker, Stanislaus Maier-Paape). Communications in Mathematical Physics, 223(3), pp. 553–582, 2001.
  51. Surface roughness in molecular beam epitaxy (with Dirk Blömker, Stanislaus Maier-Paape). Stochastics and Dynamics, 1(2), pp. 239–260, 2001.
  52. Slow motion in higher-order systems and Γ-convergence in one space dimension (with William D. Kalies, Robert C.A.M. VanderVorst). Nonlinear Analysis: Theory, Methods, and Applications, 44(1), pp. 33–57, 2001.
  53. Unexpectedly linear behavior for the Cahn-Hilliard equation (with Evelyn Sander). SIAM Journal on Applied Mathematics, 60(6), pp. 2182–2202, 2000.
  54. The Hartman-Grobman theorem for Caratheodory type differential equations in Banach spaces (with Bernd Aulbach). Nonlinear Analysis: Theory, Methods, and Applications, 40(1-8), pp. 91–104, 2000.
  55. Spinodal decomposition for multicomponent Cahn-Hilliard systems (with Stanislaus Maier-Paape, Barbara Stoth). Journal of Statistical Physics, 98(3-4), pp. 871–896, 2000.
  56. Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics (with Stanislaus Maier-Paape). Archive for Rational Mechanics and Analysis, 151(3), pp. 187–219, 2000.
  57. Monte Carlo simulations for spinodal decomposition (with Evelyn Sander). Journal of Statistical Physics 95(5-6), pp. 925–948, 1999.
  58. Dissipative quasigeostrophic dynamics under random forcing (with James R. Brannan, Jinqiao Duan). Journal of Mathematical Analysis and Applications 228(1), pp. 221–233, 1998.
  59. Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Part I: Probability and wavelength estimate (with Stanislaus Maier-Paape). Communications in Mathematical Physics 195(2), pp. 435–464, 1998.
  60. Solutions of nonlinear planar elliptic problems with triangle symmetry (with Stanislaus Maier-Paape). Journal of Differential Equations 136(1), pp. 1–34, 1997.
  61. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation (with Paul C. Fife, Hansjörg Kielhöfer, Stanislaus Maier-Paape). Physica D: Nonlinear Phenomena 100(3-4), pp. 257–278, 1997.
  62. Linearization of random dynamical systems. Dynamics Reported 4, pp. 203–269, 1995.
  63. Supersolvable and modularly complemented matroid extensions (with Günter M. Ziegler). European Journal of Combinatorics 12(4), pp. 341–360, 1991.
  64. On the chromaticity of certain subgraphs of a q-tree. Journal of Graph Theory 13(5), pp. 597–605, 1989.

Book chapters

  1. Computer-assisted bifurcation diagram validation and applications in materials science. Proceedings of Symposia in Applied Mathematics, Vol. 74, pp. 123–174. American Mathematical Society, Providence, 2018.
  2. Topological analysis of the diblock copolymer equation. In: Y. Nishiura, M. Kotani (editors), Mathematical Challenges in a New Phase of Materials Science, Springer Proceedings in Mathematics & Statistics 166, pp. 27–51, Springer-Verlag, 2016.
  3. Phase separation in stochastic Cahn-Hilliard models (with Dirk Blömker, Stanislaus Maier-Paape). Mathematical Methods and Models in Phase Transitions, edited by A. Miranville, pp. 1–41. Nova Science Publishers, 2005.
  4. Invariant foliations for Caratheodory type differential equations in Banach spaces (with Bernd Aulbach). Advances in Stability Theory at the End of the 20th Century, edited by A.A. Martynyuk, Stability and Control: Theory, Methods and Applications, Vol. 13, pp. 1–14. Taylor and Francis, London, 2003.
  5. Integral manifolds for Caratheodory type differential equations in Banach spaces (with Bernd Aulbach). Six Lectures on Dynamical Systems, edited by B. Aulbach and F. Colonius, pp. 45–119. World Scientific, Singapore, 1996.

Articles in proceedings

  1. Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence (with Brian S. Marks, Curtis R. Menyuk, John Zweck). Optical Fiber Communication Conference 2003, Technical Digest, pp. 370–372, 2003.
  2. Spinodal decomposition: A survey of recent results (with Stanislaus Maier-Paape, Evelyn Sander). In: B. Fiedler, K. Gröger, and J. Sprekels (editors), Equadiff 99, Proceedings of the International Conference on Differential Equations, Volume 2, pp. 1288–1299, World Scientific, 2000.
  3. Spinodal decomposition for the stochastic Cahn-Hilliard equation (with Dirk Blömker, Stanislaus Maier-Paape). In: B. Fiedler, K. Gröger, and J. Sprekels (editors), Equadiff 99, Proceedings of the International Conference on Differential Equations, Volume 2, pp. 1265–1267, World Scientific, 2000.
  4. Spinodal decomposition in the linear Cahn-Hilliard model (with Stanislaus Maier-Paape). Zeitschrift für Angewandte Mathematik und Mechanik 78(S3), pp. S1003–S1004, 1998.
  5. Qualitative behavior of random differential equations. In: D. Bainov and A. Dishliev (editors), Proceedings of the Fifth International Colloquium on Differential Equations, Volume 2, pp. 242–257, SCT Publishing, 1995.

Software packages

  1. ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes. Software Package, 10.5281/zenodo.14248929, 2024.
  2. isoblockval: Rigorous validation of isolating blocks (with Thomas Stephens). Software Package, 10.5281/zenodo.14229876, 2014.

Miscellaneous writings

  1. Finding attracting sets using combinatorial multivector fields (with Justin Thorpe). Accepted, but unpublished, manuscript, arXiv:2503.23079, 6 pages, 2025.
  2. Editorial: Topology in dynamics, differential equations, and data (with Sarah Day, Robert C.A.M. VanderVorst). Physica D: Nonlinear Phenomena 334(1), pp. 1–3, 2016.
  3. Review of Computational Homology by T. Kaczynski, K. Mischaikow, and M. Mrozek. SIAM Review, 48(1), pp. 202–204, 2006.

Theses

  1. Zur Linearisierung zufälliger dynamischer Systeme. Ph.D. thesis, Universität Augsburg, Germany, 172 pages, 1993.
  2. Invariante Faserbündel und topologische Äquivalenz bei dynamischen Prozessen. M.S. thesis, Universität Augsburg, Germany, 135 pages, 1991.

Manuscripts in preparation

  1. Theory and Numerics of Partial Differential Equations (with Evelyn Sander). Book manuscript, 1023 pages, in preparation.

Graduate Students, Ph.D.

  • current Bartosz Furmanek, Ph.D. in Mathematics, Jagiellonian University, in progress.
  • current Frank Pryor, Ph.D. in Mathematics, GMU, in progress.
  • 2026 Justin Thorpe: Periodic Orbits in the Setting of Combinatorial Dynamics, Ph.D. in Mathematics, GMU.
  • 2022 Peter Rizzi: On Validated Equilibria and Bifurcations in Materials Science and Stochastic Dynamics, Ph.D. in Mathematics, GMU.
  • 2017 Patrick O’Neil: Analyzing and Extending the Distance-to-Measure Gradient Flow using Higher Order Voronoi Diagrams, Ph.D. in Mathematics, GMU.
  • 2016 Thomas Stephens: Topological Methods for Evolution Equations, Ph.D. in Mathematics, GMU.
  • 2011 Gregory S. Cochran: Optimal Sampling of Random Fields for Topological Analysis, Ph.D. in Mathematics, GMU.
  • 2009 Andrew Corrigan: Kernel-Based Meshless Methods, Ph.D. in Computational Mathematics, GMU.
  • 2008 Tina R. Hartley: An Analysis of Phase Separation Processes for Stochastic and Nonlocal Extensions of the Classical Phase-Field Model, Ph.D. in Computational Mathematics, GMU.
  • 2005 Valeriy R. Korostyshevskiy: A Hermite Spectral Approach to Homoclinic Solutions of Ordinary Differential Equations, Ph.D. in Applied Mathematics, UMBC.

Graduate Students, M.S.

  • 2021 Lauren Joyave: Nonsmooth Frameworks for an Extended Budyko Model, M.S. in Mathematics, GMU.
  • 2017 Mahendra Panagoda: Swarm Dynamics and Mean-Field Games, M.S. in Mathematics, GMU.
  • 2011 Mike Atkins: Long Term Dynamics of the Di-Block Copolymer Model on Higher Dimensional Domains, M.S. in Mathematics, GMU.
  • 2008 Elan Rodan: Successive Continuation for Locating Connecting Orbits, M.S. in Mathematics, GMU.
  • 2004 Jonathan P. Desi: A Study of the Cahn-Hilliard Equation on the Unit Disk, M.S. in Applied Mathematics, UMBC.
  • 2002 Jennifer E. Deering: Computation of the Bifurcation Structure of the Cahn-Hilliard Equation, M.S. in Applied Mathematics, UMBC.

Undergraduate Students

  • 2025 William Carey: Predicting Flood Zones Using Topological Data Analysis, MEGL Undergraduate Research Project, GMU.
  • 2025 Kyle Hess: Predicting Flood Zones Using Topological Data Analysis, MEGL Undergraduate Research Project, GMU.
  • 2025 Marty Roger: Predicting Flood Zones Using Topological Data Analysis, MEGL Undergraduate Research Project, GMU.
  • 2018 Micheal Belete: Stable Annulus Solution for the Diblock Copolymer Equation, EXTREEMS Undergraduate Research Project, GMU.
  • 2018 Andrew Hornstra: Diblock Copolymer Modeling in 3D, EXTREEMS Undergraduate Research Project, GMU.
  • 2017 Hye Kyung Kim: Dynamics of Red Coral Populations, EXTREEMS Undergraduate Research Project, GMU.
  • 2016 Harout Boujakjian: Meta-Stability of the Allen-Cahn Fractional Differential Equation, MEGL Undergraduate Research Project, GMU.
  • 2016 Kathleen McLane: Meta-Stability of the Allen-Cahn Fractional Differential Equation, MEGL Undergraduate Research Project, GMU.
  • 2016 Conor Nelson: Meta-Stability of the Allen-Cahn Fractional Differential Equation, MEGL Undergraduate Research Project, GMU.
  • 2015 James Trichilo: Frequency Domain Analysis of the Diblock Copolymer Equation, EXTREEMS Undergraduate Research Project, GMU.
  • 2014 Mahmoud Namazi: Nucleation in a Two-Component Metal Alloy, CSUMS Undergraduate Research Project, GMU.
  • 2013 Kalea Sebesta: Nucleation in a Two-Component Metal Alloy, REU Undergraduate Research Project, GMU.
  • 2011 Ian Johnson: Continuation Analysis for the Diblock-Copolymer Equation in One Dimension, CSUMS Undergraduate Research Project, GMU.
  • 2010 Olga Stulov: Stability of Equilibria in 1D for the Diblock-Copolymer Equation, REU Undergraduate Research Project, GMU.
  • 2010 James O’Beirne: The Dynamics of Nucleation in Stochastic Cahn-Morral Systems, CSUMS Undergraduate Research Project, GMU.
  • 2009 Colleen Ackerman: The Dynamics of Nucleation in Stochastic Cahn-Morral Systems, REU Undergraduate Research Project, GMU.
  • 2009 William Hardesty: The Dynamics of Nucleation in Stochastic Cahn-Morral Systems, REU Undergraduate Research Project, GMU.
  • 2009 Thomas Stephens: Nonlocal Extensions of the Classical Phase Field Model, CSUMS Undergraduate Research Project, GMU.
  • 2008 Hanein Edrees: The Dynamics of Nucleation in Stochastic Cahn-Morral Systems, CSUMS Undergraduate Research Project, GMU.
  • 2008 Jonathan Price: The Dynamics of Nucleation in Stochastic Cahn-Morral Systems, CSUMS Undergraduate Research Project, GMU.
  • 2005 Ravi Kappiyoor: Microstructure Response Isosurfaces for Low Thermal Expansion Polycrystals, Summer Research Project, GMU & NIST.
  • 2003 Eli Leyman: Solidification Phenomena in Pure Materials, Summer Research Project, GMU.
  • 2003 Jonathan P. Desi: A Numerical Study of Nucleation in Stochastic Cahn-Morral Systems, Undergraduate Senior Thesis, UMBC.

Courses Taught

George Mason University

  • Fall 2026
    • Math 214 Elementary Differential Equations
  • Summer 2026
    • Math 999 Doctoral Dissertation
  • Spring 2026
    • Math 214 Elementary Differential Equations
    • Math 998 Dissertation Proposal
    • Math 999 Doctoral Dissertation
  • Fall 2025
    • Math 214 Elementary Differential Equations
    • Math 413 Modern Applied Mathematics I
    • Math 697 Introduction to Conley Theory
    • Math 999 Doctoral Dissertation
  • Spring 2025
    • Math 214 Elementary Differential Equations
    • Math 689 Applied and Computational Topology
    • Math 491 Predicting Flood Zones Using Topological Data Analysis
    • Math 697 Combinatorial Topological Dynamics
    • Math 999 Doctoral Dissertation
  • Fall 2024
    • Math 675 Linear Analysis
    • Math 697 Global Dynamics via Analysis and Topology
    • Math 999 Doctoral Dissertation
  • Spring 2024
    • Math 686 Numerical Solution of Differential Equations
    • Math 697 Bifurcation Theory in Partial Differential Equations
    • Math 697 Computer Validation
    • Math 999 Doctoral Dissertation
  • Fall 2023
    • Math 213 Analytic Geometry and Calculus III
    • Math 413 Modern Applied Mathematics I
    • Math 999 Doctoral Dissertation
  • Spring 2023
    • Math 214 Elementary Differential Equations
    • Math 631 Topology
    • Math 999 Doctoral Dissertation
  • Fall 2022
    • Math 214 Elementary Differential Equations
    • Math 678 Partial Differential Equations
    • Math 999 Doctoral Dissertation
  • Summer 2022
    • Math 999 Doctoral Dissertation
  • Spring 2022
    • Math 999 Doctoral Dissertation (two sections)
  • Fall 2021
    • Math 213 Analytic Geometry and Calculus III
    • Math 413 Modern Applied Mathematics I
    • Math 998 Dissertation Proposal
    • Math 999 Doctoral Dissertation
  • Spring 2021
    • Math 213 Analytic Geometry and Calculus III
    • Math 431 Topology
    • Math 697 Mathematics & Climate (Reading course)
    • Math 998 Dissertation Proposal (two sections)
  • Fall 2020
    • Math 213 Analytic Geometry and Calculus III (two sections)
    • Math 998 Dissertation Proposal
  • Spring 2020
    • Math 213 Analytic Geometry and Calculus III
    • Math 625 Numerical Linear Algebra
    • Math 697 Computational Topology (Reading course)
  • Fall 2019
    • Math 213 Analytic Geometry and Calculus III
    • Math 675 Linear Analysis I
    • Math 697 Rigorous Computations for PDEs (Reading course)
  • Summer 2019
    • Math 697 Mathematics & Climate (Reading course)
  • Spring 2019
    • Math 213 Analytic Geometry and Calculus III
    • Math 784 Nonlinear Functional Analysis
    • Math 697 Seminar on Mathematics & Climate
  • Fall 2018
    • Math 478 Introduction to PDEs with Numerical Methods
    • Math 677 Ordinary Differential Equations
  • Spring 2018
    • Math 406 Honors Thesis in Mathematics II
    • Math 689 Bifurcation Theory
  • Fall 2017
    • Math 213 Analytic Geometry and Calculus III
    • Math 405 Honors Thesis in Mathematics
    • Math 675 Linear Analysis I
  • Spring 2017
    • Math 214 Elementary Differential Equations
    • Math 784 Nonlinear Functional Analysis
  • Fall 2016
    • Math 213 Analytic Geometry and Calculus III
    • Math 478 Introduction to PDEs with Numerical Methods
  • Spring 2016
    • Math 213 Analytic Geometry and Calculus III
    • Math 625 Numerical Linear Algebra
  • Fall 2015
    • Math 213 Analytic Geometry and Calculus III
    • Math 405 Honors Thesis in Mathematics
    • Math 677 Ordinary Differential Equations
  • Spring 2015
    • Math 446 Numerical Analysis I
    • Math 689 Computational Topology
    • Math 795 Graduate Seminar
  • Fall 2014
    • Math 213 Analytic Geometry and Calculus III
    • Math 478 Introduction to PDEs with Numerical Methods
  • Fall 2013
    • Math 214 Elementary Differential Equations
    • Math 678 Partial Differential Equations
  • Summer 2013
    • Math 478 Introduction to PDEs with Numerical Methods
  • Spring 2013
    • Math 214 Elementary Differential Equations
    • Math 784 Nonlinear Functional Analysis
  • Spring 2012
    • Math 315 Advanced Calculus I
    • Math 625 Numerical Linear Algebra
  • Fall 2011
    • Math 213 Analytic Geometry and Calculus III
    • Math 781 Advanced Methods in Applied Mathematics
  • Summer 2011
    • Math 478 Introduction to PDEs with Numerical Methods
  • Spring 2011
    • Math 125 Discrete Mathematics I
    • Math 689 Evolution Equations
  • Fall 2010
    • Math 675 Linear Analysis I
  • Summer 2010
    • Math 493 Topics in Applicable Mathematics
  • Spring 2010
    • Math 114 Analytic Geometry and Calculus II
    • Math 686 Numerical Solution of Differential Equations
  • Fall 2009
    • Math 213 Analytic Geometry and Calculus III
    • Math 781 Advanced Methods in Applied Mathematics
  • Spring 2009
    • Math 213 Analytic Geometry and Calculus III
    • Math 625 Numerical Linear Algebra
  • Fall 2008
    • Math 685 Numerical Analysis
  • Spring 2008
    • Math 214 Elementary Differential Equations
    • Math 678 Partial Differential Equations
  • Fall 2007
    • Math 677 Ordinary Differential Equations
  • Summer 2007
    • Math 493 Topics in Applicable Mathematics
  • Spring 2007
    • Math 625 Numerical Linear Algebra
    • Math 689 Nonlinear Functional Analysis
  • Spring 2006
    • Math 114 Analytic Geometry and Calculus II
    • Math 686 Numerical Solution of Differential Equations
  • Fall 2005
    • Math 685 Numerical Analysis
  • Spring 2005
    • Math 108 Introductory Calculus with Business Applications
    • Math 214 Elementary Differential Equations
  • Fall 2004
    • Math 113 Analytic Geometry and Calculus I
    • Math 689 Computational Algebraic Topology
  • Fall 2003
    • Math 111 Linear Mathematical Modeling
    • Math 675 Linear Analysis I
  • Spring 2003
    • Math 414 Modern Applied Mathematics II
    • Math 673 Dynamical Systems
  • Fall 2002
    • Math 213 Analytic Geometry and Calculus III
    • Math 446 Numerical Analysis I

University of Maryland, Baltimore County

  • Spring 2002
    • Math 302 Introduction to Mathematical Analysis II
    • Math 601 Measure Theory
  • Fall 2001
    • Math 301 Introduction to Mathematical Analysis I (two sections)
    • Math 699 Introduction to Conley Index Theory (Reading course)
  • Spring 2001
    • Math 302 Introduction to Mathematical Analysis II
    • Math 612 Ordinary Differential Equations and Dynamical Systems
    • Math 699 Introduction to Algebraic Topology (Reading course)
  • Fall 2000
    • Math 221 Introduction to Linear Algebra
    • Math 301 Introduction to Mathematical Analysis I
    • Math 699 Practical Bifurcation and Stability Analysis (Reading course)
  • Spring 2000
    • Math 225 Introduction to Differential Equations
    • Math 710 Nonlinear Functional Analysis
  • Fall 1999
    • Math 251 Multivariable Calculus
    • Math 251 Multivariable Calculus (Honors section)
    • Math 614 Partial Differential Equations
    • Math 699 Introduction to Conley Index Theory (Reading course)
  • Spring 1999
    • Math 152 Calculus and Analytic Geometry II
    • Math 611 Applied Analysis
    • Math 699 Introduction to Algebraic Topology (Reading course)
  • Fall 1998
    • Math 151 Calculus and Analytic Geometry I

Professional Activities

  • Editorial Board Member of

    • Frontiers in Applied Dynamical Systems (since 2015),
    • SIAM Journal on Applied Dynamical Systems (since 2015),
    • Discrete and Continuous Dynamical Systems, Series B (since 2012),
    • Mathematical Methods in the Applied Sciences (2009–2024),
    • Physica D: Nonlinear Phenomena (2010–2023),
    • Discrete and Continuous Dynamical Systems, Series S (2007–2012).

  • Referee for Advances in Computational Mathematics, Applied Mathematics and Computation, Communications on Pure and Applied Mathematics, Computational Geometry: Theory and Applications, Computer Methods in Applied Mechanics and Engineering, Discrete and Continuous Dynamical Systems, European Journal of Applied Mathematics, Foundations of Computational Mathematics, Indagationes Mathematicae, International Journal of Mathematics and Mathematical Sciences, Interfaces and Free Boundaries, Journal of Computational and Applied Mathematics, Journal of Computational Dynamics, Journal of Differential Equations, Journal of Dynamics and Differential Equations, Journal of Graph Theory, Journal of Mathematical Analysis and Applications, Journal of Physics A, Journal of Sound and Vibration, Nonlinear Analysis, Nonlinearity, Physica D, Proceedings of the American Mathematical Society, Proceedings of Symposia in Applied Mathematics, Random & Computational Dynamics, SIAM Journal on Applied Dynamical Systems, SIAM Journal on Applied Mathematics, SIAM Journal on Mathematical Analysis, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, SIAM Review, Stochastics and Dynamics, Stochastics and Stochastics Reports, Topological Methods in Nonlinear Analysis, Transactions of the AMS, Zeitschrift für Angewandte Mathematik und Mechanik.

  • Book proposal reviewer for American Mathematical Society, Cambridge University Press, Springer-Verlag.

  • Panelist for the National Science Foundation.

  • Grant reviewer for National Science Foundation, Department of Energy, Chilean Science Foundation, Dutch Science Foundation, Israel Science Foundation, Portuguese Science Foundation, National Science Centre of Poland, Simons Foundation.

  • Co-Editor of a special issue of Physica D on “Topology in dynamics, differential equations, and data” (2014 – 2016).

  • Member of various conference committees:

    • The 15th AIMS Conference, Athens, Greece (July 2026). Global Organizing Committee.
    • International Conference Applied Topology in Poznan 2025, Poznan, Poland (July 2025). Scientific Committee.
    • International Conference DyToComp 2025: Dynamics, Topology, and Computations, Bedlewo, Poland (June 2025). Scientific Committee.
    • Workshop on Combinatorial Topological Dynamics, Krakow, Poland (May 2025). Scientific Committee.

  • Organizer of various minisymposia, special sessions, and workshops:

    • Workshop on Interactions of Topological Data Analysis and Combinatorial Topological Dynamics, BIRS, Banff, Canada (August 2027).
    • Workshop on Combinatorial Topological Framework for Nonlinear Dynamics, CRM, Montreal, Canada (October 2024).
    • Minisymposium on Combinatorial Topological Dynamics, ICIAM 23: International Congress on Industrial and Applied Mathematics, Tokyo, Japan (August 2023).
    • Session on Computational Dynamics in the Context of Data, ICMC Summer Meeting on Differential Equations, Sao Carlos, Brazil (February 2019).
    • Workshop on Combinatorics, Enumeration, and Invariant Theory, George Mason University, Fairfax, Virginia (March 2010).
    • Workshop on Computational Topology and Dynamics, Montana State University, Bozeman, Montana (August 2008).
    • Minisymposium on Computational Topology and Dynamics, ICIAM 07: 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland (July 2007).
    • Minisymposium on Stochastic Partial Differential Equations and Pattern Formation, SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 2007).
    • Special session on Formation and Dynamics of Patterns in Evolution Equations, AIMS Conference on Dynamical Systems, Differential Equations and Applications, Poitiers, France (June 2006).
    • Workshop on Computational Homology and Materials Science, Georgia Institute of Technology, Atlanta, Georgia (February 2006).
    • Minisymposium on Topological Analysis of Patterns, SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 2005).
    • Minisymposium on Stochastic Differential Equations: Dynamics and Applications, SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 2001).
    • Minisymposium on Pattern formation in the Cahn-Hilliard model, SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 1999).

  • Invited lectures and conference presentations

    1. “Computer-assisted bifurcation point validation.” 15th AIMS Conference, Athens, Greece (July 7, 2026).
    2. “Connection matrices in combinatorial topological dynamics.” Combinatorial Topological Dynamics Workshop, Jagiellonian University, Krakow, Poland (May 26, 2025).
    3. “Bifurcation point validation using extended systems.” Mathematics Colloquium, Howard University, Washington, DC (November 15, 2024).
    4. “Combinatorial topological dynamics via multivectors.” Combinatorial Topological Framework for Nonlinear Dynamics, CRM, Montreal, Canada (October 11, 2024).
    5. “Combinatorial topological dynamics.” XXV Workshop for Young Mathematicians, Jagiellonian University, Krakow, Poland (lecture series, September 24 and 25, 2024).
    6. “Bifurcation point validation using extended systems.” Computer Assisted Proofs in Nonlinear Analysis, CRM, Montreal, Canada (September 11, 2024).
    7. “Capturing invariance in flows and combinatorial vector fields.” Topology Seminar, Universidad de Buenos Aires, Online Talk (November 15, 2023).
    8. “Bifurcation points induced by cyclic symmetries.” 29th Nordic Congress of Mathematicians with EMS, Aalborg, Denmark (July 5, 2023).
    9. “Bifurcation points induced by cyclic symmetries.” Computational Mathematics Seminar, Jagiellonian University, Krakow, Poland (May 11, 2023).
    10. “Bifurcation points induced by cyclic symmetries.” Applied & Computational Mathematics Seminar, Rutgers University, Piscataway, New Jersey (April 25, 2023).
    11. “Combinatorial topological dynamics.” Applied & Computational Mathematics Seminar, Georgia Institute of Technology, Atlanta, Georgia (November 7, 2022).
    12. “Combinatorial topological dynamics.” DyToComp 2022: Dynamics, Topology, and Computations, Bedlewo, Poland (June 21, 2022).
    13. “From discrete Morse theory to combinatorial topological dynamics” (Tutorial talk). GETCO: 11th International Conference on Geometric and Topological Methods in Computer Science, Paris, France (May 31, 2022).
    14. “Equilibrium validation in models for pattern formation based on Sobolev embeddings.” SIAM Conference on Applications of Dynamical Systems, Virtual Conference (May 23, 2021).
    15. “Bifurcation points in the Ohta-Kawasaki model.” CRM CAMP in Nonlinear Analysis Seminar, Online Talk (May 18, 2021).
    16. “A computer-assisted study of the diblock copolymer model.” Mathematics Colloquium, Swansea University, Swansea, Wales (December 12, 2019).
    17. “Combinatorial topological dynamics.” EquaDiff 2019, Leiden, Netherlands (July 8, 2019).
    18. “Creating semiflows on simplicial complexes from combinatorial vector fields.” Seminar on Computational Mathematics, Jagiellonian University, Krakow, Poland (May 16, 2019).
    19. “Creating semiflows on simplicial complexes from combinatorial vector fields.” Combinatorial/Algebraic Topological Approaches to Nonlinear and Data Driven Dynamics, CRM, Montreal, Canada (April 16, 2019).
    20. “Capturing invariance in flows and combinatorial vector fields.” Topology, Algebraic Geometry and Dynamics Seminar, George Mason University, Fairfax, Virginia (March 22, 2019).
    21. “Combinatorial topological dynamics I: Linking combinatorial and classical dynamics.” ICMC Summer Meeting on Differential Equations, Sao Carlos, Brazil (February 5, 2019).
    22. “Bifurcation diagram verification for the diblock copolymer model.” Applied Mathematics Colloquium, New Jersey Institute of Technology, Newark, New Jersey (November 30, 2018).
    23. “Combinatorial topological dynamics I: Linking combinatorial and classical dynamics.” Algebraic Topology in Data and Dynamics, Montana State University, Bozeman, Montana (July 10, 2018).
    24. “Automatic differentiation, interval arithmetic, and computer-assisted proofs.” EXTREEMS Tutorial, George Mason University, Fairfax, Virginia (June 11, 2018).
    25. “Bifurcation diagram verification for the diblock copolymer model.” DynamIC Seminar, Imperial College, London, England (November 21, 2017).
    26. “Automatic differentiation, interval arithmetic, and computer-assisted proofs.” EXTREEMS Tutorial, George Mason University, Fairfax, Virginia (June 5-7, 2017).
    27. “Rigorous continuation of equilibria and bifurcation points in the diblock copolymer equation.” BIRS Workshop on Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics, Banff, Canada (May 8, 2017).
    28. “Topological microstructure analysis using persistence landscapes.” Joint Mathematics Meetings, Atlanta, Georgia (January 4, 2017).
    29. “Computer-assisted bifurcation diagram validation and applications in materials science.” Applied Mathematics Colloquium, University of Maryland, Baltimore County, Maryland (December 9, 2016).
    30. “Topological quantification of microstructures.” CMaSC/CDS Colloquium, George Mason University, Fairfax, Virginia (November 21, 2016).
    31. “Automatic differentiation, interval arithmetic, and computer-assisted proofs.” EXTREEMS Tutorial, George Mason University, Fairfax, Virginia (June 3, 2016).
    32. “Rigorous level curve enclosures: From isolating blocks to bifurcation diagrams.” Winter School on Computational Mathematics, Bedlewo, Poland (lecture series, February 8, 10, and 11, 2016).
    33. “Computer-assisted bifurcation diagram validation and applications in materials science.” AMS Short Course on Rigorous Numerics in Dynamics, Seattle, Washington (January 5, 2016).
    34. “Computer-assisted proofs in differential equations.” GMUMS Seminar, George Mason University, Fairfax, Virginia (November 20, 2015).
    35. “Rigorous validation of isolating blocks for flows.” DyToComp 2015: Dynamics, Topology, and Computations, Bedlewo, Poland (June 19, 2015).
    36. “Dynamics of diblock copolymers.” EXTREEMS Faculty Talk, George Mason University, Fairfax, Virginia (May 26, 2015).
    37. “Dynamics of phase separation.” DARPA Dynamics, Geometry and Big Data Sets Workshop, Arlington, Virginia (May 5, 2015).
    38. “Dynamics of diblock copolymers: A case study in computer-assisted proofs.” Colloquium, Universität Augsburg, Germany (April 21, 2015).
    39. “Droplet formation in binary and ternary stochastic systems.” X Americas Conference on Differential Equations and Nonlinear Analysis, Buenos Aires, Argentina (February 19, 2015).
    40. “Multistability and long-term dynamics of the diblock copolymer model.” Mathematical Challenge to a New Phase of Materials Science, RIMS, Kyoto, Japan (August 8, 2014).
    41. “Nucleation in three-component Cahn-Morral systems.” Sapporo Summer Conference on Dynamics of Patterns in Materials Science, Hokkaido University, Sapporo, Japan (July 31, 2014).
    42. “Phase separation phenomena and partial attractor structure.” From Topological to Stochastic Techniques in Dynamical Systems, Lorentz Center, Leiden, Netherlands (June 23, 2014).
    43. “Droplet formation in binary and ternary stochastic systems.” Applied Mathematics Seminar, McGill University, Montreal, Canada (April 7, 2014).
    44. “Multistability in the diblock copolymer model.” RIMS Workshop on New Directions in Applied Dynamical Systems, Kyoto, Japan (March 13, 2014).
    45. “Stochastic dynamics of droplet formation.” RIMS Workshop on New Directions in Applied Dynamical Systems, Kyoto, Japan (March 12, 2014).
    46. “Randomized adaptive topology validation for nodal domains.” IMA Workshop on Algebraic Topology in Dynamics, Differential Equations, and Experimental Data, Minneapolis, Minnesota (February 11, 2014).
    47. “Partial attractor structure — Two problems from materials science.” AIM Workshop on Rigorous Computation for Infinite Dimensional Nonlinear Dynamics, Palo Alto, California (August 29, 2013).
    48. “An introduction to stochastic differential equations.” REU/URCM Seminar Series, George Mason University, Fairfax, Virginia (June 13, 2013).
    49. “Droplet formation in binary and ternary stochastic systems.” IMA Special Workshop on Interactions among Localized Patterns in Dissipative Systems, Minneapolis, Minnesota (June 4, 2013).
    50. “An introduction to stochastic ordinary differential equations.” IMA Tutorial on Stochastic Differential Equations, Minneapolis, Minnesota (January 11, 2013, two talks).
    51. “Topology-guided sampling of complicated random patterns.” Dynamics and Patterns Seminar, University of Minnesota, Minneapolis, Minnesota (November 5, 2012).
    52. “Stochastic nucleation dynamics.” IMA Dynamical Systems Seminar, Minneapolis, Minnesota (October 4, 2012).
    53. “Randomized adaptive topology validation for excursion sets.” DyToComp 2012: Dynamics, Topology, and Computations, Bedlewo, Poland (June 25, 2012).
    54. “Uncovering the bifurcation structure of the diblock copolymer model.” IV. Developers Workshop on the Conley-Morse Database Project, Kauai, Hawaii (March 21, 2012).
    55. “Stochastic nucleation dynamics.” Spring Eastern Sectional Meeting of the American Mathematical Society, Washington, DC (March 17, 2012).
    56. “Stochastic nucleation dynamics.” Oberseminar, Universität Augsburg, Germany (September 20, 2011).
    57. “Topological quantification of microstructures.” Workshop on Microstructure Modeling in Drug Eluting Coatings, US Food and Drug Administration, Silver Spring, Maryland (September 6, 2011).
    58. “Stochastic nucleation dynamics.” Foundations of Computational Mathematics, Budapest, Hungary (July 12, 2011).
    59. “An introduction to stochastic differential equations.” URCM Seminar Series, George Mason University, Fairfax, Virginia (July 7, 2011).
    60. “Probabilistic and numerical validation of homology computations for nodal domains.” Jagiellonian University, Krakow, Poland (October 21, 2010).
    61. “Topology-guided sampling of Gaussian random fields.” Isaac Newton Institute, Cambridge, United Kingdom (June 25, 2010).
    62. “The dynamics of nucleation in stochastic Cahn-Morral systems.” Joint SIAM/RSME-SCM-SEMA Meeting, Barcelona, Spain (May 31, 2010).
    63. “Dynamics and morphology of phase separation.” SIAM-GMU Faculty Research Symposium, Fairfax, Virginia (November 6, 2009).
    64. “The dynamics of nucleation in stochastic Cahn-Morral systems.” Fall Southeastern Sectional Meeting of the American Mathematical Society, Boca Raton, Florida (October 31, 2009).
    65. “The dynamics of nucleation in stochastic Cahn-Morral systems.” Jagiellonian University, Krakow, Poland (October 13, 2009).
    66. “Homology of complicated and random evolving patterns.” Sandia CSRI Workshop on Combinatorial Algebraic Topology, Santa Fe, New Mexico (August 29, 2009).
    67. “The dynamics of nucleation in stochastic Cahn-Morral systems.” International Conference on Random Dynamical Systems, Chern Institute of Mathematics, Tianjin, China (June 8, 2009).
    68. “Counting holes in microstructures: Topology and materials.” REU & URCM Research Seminar Series, George Mason University, Fairfax, Virginia (June 3, 2009).
    69. “Topology-guided sampling of Gaussian random fields.” Workshop on Topology, Institute for Advanced Study, Princeton, New Jersey (April 1, 2009).
    70. “Spinodal decomposition: Complex patterns and topology.” Soft Matter Laboratory, Yale University, New Haven, Connecticut (February 24, 2009).
    71. “Determining the topology of random evolving patterns from discretizations.” LCDS Seminar, Brown University, Providence, Rhode Island (February 23, 2009).
    72. “Homology computations for random nodal domains.” Annual Meeting of the American Mathematical Society, Washington, DC (January 6, 2009).
    73. “Homology computations for random nodal domains.” Applied Mathematics Seminar, George Washington University, Washington, DC (November 18, 2008).
    74. “Verified homology computations for nodal domains.” Computational Topology and Dynamics Workshop, Bozeman, Montana (August 12, 2008).
    75. “Topology-guided sampling of complicated random patterns.” Foundations of Computational Mathematics, Hong Kong, China (June 16, 2008).
    76. “Topology-guided sampling of complicated random patterns.” Rocky Mountain Conference on Dynamical Systems, Park City, Utah (May 16, 2008).
    77. “Topology-guided sampling of complicated random patterns.” Oberseminar, Universität Augsburg, Germany (April 14, 2008).
    78. “Counting holes in microstructures: Topology and materials.” Osher Lifelong Learning Institute, Fairfax, Virginia (April 1, 2008).
    79. “Homological analysis of complicated random patterns.” Applied Dynamics Seminar, University of Maryland, College Park, Maryland (February 14, 2008).
    80. “Topological quantification of complex microstructures.” US Food and Drug Administration, Silver Spring, Maryland (January 31, 2008).
    81. “Homological analysis of complicated random patterns.” Mathematics Colloquium, Virginia Tech, Blacksburg, Virginia (November 30, 2007).
    82. “Homological analysis of complicated random patterns.” CSUMS Lecture, College of William and Mary, Williamsburg, Virginia (November 12, 2007).
    83. “Counting holes in microstructures: Topology and materials.” Science Showcase for High End High School Students, Fairfax, Virginia (October 19, 2007).
    84. “Homological analysis of complicated random patterns.” GMU Applied and Computational Mathematics Seminar, Fairfax, Virginia (October 12, 2007).
    85. “Uncertainty quantification for homology computations.” ICIAM 07: 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland (July 20, 2007).
    86. “Der Cahn-Hilliard Attraktor in zwei Raumdimensionen.” Oberseminar, Universität Augsburg, Germany (July 12, 2007).
    87. “Determining the topology of complex stochastic patterns from finite discretizations.” SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 30, 2007).
    88. “Homological characterization of patterns.” Computational Homology and Fluid Dynamics Workshop, Atlanta, Georgia (March 1, 2007).
    89. “Structure of the attractor of the Cahn-Hilliard equation on a square.” Seminar, Kyoto University, Kyoto, Japan (February 12, 2007).
    90. “Homological analysis of complex transient patterns via discretizations.” Workshop on Topological and Computational Approaches to Dynamical Systems and Applications, Kyoto, Japan (February 9, 2007).
    91. “Complex transient patterns and their topology.” Winter Meeting of the Canadian Mathematical Society, Toronto, Canada (December 11, 2006).
    92. “Probabilistic and numerical validation of homology computations for nodal domains.” Dynamics and Control Seminar, Rutgers University, Piscataway, New Jersey (October 24, 2006).
    93. “Probabilistic and numerical validation of homology computations for nodal domains.” Workshop on Application of Topology in Science and Engineering, MSRI, Berkeley, California (September 18, 2006).
    94. “Zur Homologie von Knotengebieten zufälliger Fourierreihen.” Universität Augsburg, Germany (June 19, 2006).
    95. “On the accuracy of homology computations for nodal domains.” DyToComp 2006: Dynamics, Topology, and Computations, Bedlewo, Poland (June 6, 2006).
    96. “Topological quantification of complex microstructures.” Day of Computational Mathematics, Nowy Sacz, Poland (June 2, 2006).
    97. “Computational homology and the evolution of complex patterns.” Graduate Seminar, George Mason University, Fairfax, Virginia (April 26, 2006).
    98. “Complex transient patterns and their homology.” Duke University, Durham, North Carolina (April 3, 2006).
    99. “Computational homology and the evolution of complex patterns.” College of William and Mary, Williamsburg, Virginia (March 24, 2006).
    100. “Computational homology and the evolution of complex patterns.” Applied Mathematics Colloquium, New Jersey Institute of Technology, Newark, New Jersey (February 24, 2006).
    101. “Homological characterization of patterns in phase separation.” Workshop on Computational Homology and Materials Science, Atlanta, Georgia (February 4, 2006).
    102. “Computational homology tutorial: Accuracy of homology computations.” Workshop on Computational Homology and Materials Science, Atlanta, Georgia (February 2, 2006).
    103. “On the accuracy of homology computations for nodal domains.” Georgia Institute of Technology, Atlanta, Georgia (December 1, 2005).
    104. “Computational approaches to phase separation dynamics.” Third Pacific Rim Conference on Mathematics, Fudan University, Shanghai, China (August 18, 2005).
    105. “Evolution of complex transient patterns.” Mini-Symposium on Nonlinear Analysis and Applications, Augsburg, Germany (June 24, 2005).
    106. “The effects of noise on transient pattern formation.” SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 26, 2005).
    107. “Residual stress networks in polycrystalline materials: Their origin and character.” SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (May 23, 2005).
    108. “Long-term dynamics of the Cahn-Hilliard equation.” University of Maryland, Baltimore County, Maryland (May 2, 2005).
    109. “Algebraic topology and the evolution of complex patterns.” University of Maryland, Baltimore County, Maryland (April 15, 2005).
    110. Lecture series at the summer school on “Conley-Index and Computational Homology.” Pappenheim, Germany (September 19–24, 2004).
    111. “Stochastic Cahn-Hilliard dynamics.” Fifth International Conference on Dynamical Systems and Differential Equations, Pomona, California (June 16, 2004).
    112. “A probabilistic approach to transient pattern formation.” SIAM Conference on Mathematical Aspects of Materials Science, Los Angeles, California (May 26, 2004).
    113. “Evolution of pattern complexity in Cahn-Hilliard models.” SIAM Conference on Mathematical Aspects of Materials Science, Los Angeles, California (May 25, 2004).
    114. “Higher-dimensional Cahn-Hilliard-Cook dynamics.” Georgia Institute of Technology, Atlanta, Georgia (April 19, 2004).
    115. “Cahn-Hilliard dynamics in higher dimensions.” Hokkaido University, Sapporo, Japan (March 18, 2004).
    116. “Stochastic Cahn-Hilliard dynamics.” US-Japan Workshop on Dynamics and Computation, Shonan, Japan (March 9, 2004).
    117. “Stochastic Cahn-Hilliard dynamics.” University of Maryland, College Park, Maryland (February 26, 2004).
    118. “Pattern formation in Cahn-Hilliard-type models.” NIST, Gaithersburg, Maryland (February 17, 2004).
    119. “Random sums and transient pattern formation.” Michigan State University, East Lansing, Michigan (January 13, 2004).
    120. “Pattern formation in Cahn-Hilliard-type models.” Laboratory for Computer Design of Materials, George Mason University, Fairfax, Virginia (October 6, 2003).
    121. “Transient pattern formation in the Cahn-Hilliard-Cook model.” NSF-CBMS Conference on Stochastic Partial Differential Equations and their Applications, Chicago, Illinois (May 22, 2003).
    122. “Random sums and transient pattern formation.” Georgia Institute of Technology, Atlanta, Georgia (March 27, 2003).
    123. “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence.” Optical Fiber Communication Conference 2003, Atlanta, Georgia (March 26, 2003).
    124. “Random sums and transient pattern formation.” Universität Augsburg, Germany (June 25, 2002).
    125. “Random sums and transient pattern formation.” RWTH Aachen, Germany (June 18, 2002).
    126. “Stochastic phenomena in pattern formation mechanisms.” George Mason University, Fairfax, Virginia (March 19, 2002).
    127. “Transient pattern formation in parabolic problems.” Georgetown University, Washington, DC (October 12, 2001).
    128. “Pattern formation in metal alloys.” Physics Department, University of Maryland, Baltimore County, Baltimore, Maryland (April 4, 2001).
    129. “Transient pattern formation in metal alloys.” Ohio State University, Columbus, Ohio (November 30, 2000).
    130. “Transient pattern formation in the Cahn-Hilliard model.” University of Maryland, College Park, Maryland (May 15, 2000).
    131. “Spinodal decomposition for the Cahn-Hilliard model.” EquaDiff 99, Berlin, Germany (August 2, 1999).
    132. “Introduction to random dynamical systems.” George Mason University, Fairfax, Virginia (November 20, 1998).
    133. “Pattern formation in metal alloys.” SUNY at Buffalo, Buffalo, New York (November 12, 1998).
    134. “Spinodal decomposition for multi-component Cahn-Hilliard systems.” Third Americas Conference on Differential Equations and Nonlinear Analysis, Atlanta, Georgia (September 12, 1998).
    135. “Pattern formation in higher-order parabolic differential equations.” UMBC, Baltimore, Maryland (March 6, 1998).
    136. “Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions.” Workshop on interfaces and parabolic regularisation, Leiden University, Netherlands, (November 6, 1997).
    137. “Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions.” AMS 1997 Fall Central Sectional Meeting, Milwaukee, Wisconsin (October 25, 1997).
    138. “Slow motion in higher-order systems and Γ-convergence in one space dimension.” AMS 1997 Fall Southeastern Sectional Meeting, Atlanta, Georgia (October 18, 1997).
    139. “Spinodal decomposition for the Cahn-Hilliard equation.” Georgia Institute of Technology, Atlanta, Georgia (October 9, 1997).
    140. “Slow motion in higher-order systems and Γ-convergence in one space dimension.” Large time behavior in dynamical systems: Analysis and numerics, Oberwolfach, Germany (August 1, 1997).
    141. “Slow motion in higher-order parabolic equations.” Third European conference on elliptic and parabolic problems, Pont-a-Mousson, France (June 16, 1997).
    142. “Slow motion and pattern formation in higher-order parabolic equations.” University of Utah, Salt Lake City, Utah (February 7, 1997).
    143. “Slow motion and pattern formation in higher-order parabolic equations.” Brigham Young University, Provo, Utah (February 6, 1997).
    144. “Pattern formation in the Cahn-Hilliard equation.” Clemson University, Clemson, South Carolina (May 30, 1996).
    145. “Slow motion in higher-order singularly perturbed equations.” Center for Applied Mathematics, Cornell University, Ithaca, New York (May 17, 1996).
    146. “Construction of doubly periodic solutions of nonlinear planar elliptic equations with certain nodal domains” (poster session). Callaway Gardens, Pine Mountain, Georgia (March 10, 1996).
    147. “Introduction to random dynamical systems.” Georgia Institute of Technology, Atlanta, Georgia (lecture series, November 14, 21, and 28, 1995, January 23 and 30, 1996).
    148. “Linearization of random dynamical systems.” Georgia Institute of Technology, Atlanta, Georgia (November 16, 1995).
    149. “Stationary solutions of the Cahn-Hilliard equation in two dimensions.” Georgia Institute of Technology, Atlanta, Georgia (September 28, 1995).
    150. “Qualitative behavior of random differential equations.” Fifth international colloquium on differential equations, University of Plovdiv, Bulgaria (August 20, 1994).
    151. “Linearization of random dynamical systems.” Universität München, Germany (July 25, 1994).
    152. “Linearization of random dynamical systems — an approach via nonautonomous random difference equations.” First international conference on difference equations, Trinity University – San Antonio, Texas (May 26, 1994).
    153. “A generalized Hartman-Grobman theorem for random dynamical systems.” Workshop “A day full of randomness,” Universität Bremen, Germany (June 4, 1993).
    154. “A Hartman-Grobman theorem for discrete random dynamical systems.” Universität Bremen, Germany (January 7, 1993).
    155. “Matroid extensions.” Fourth international symposium on graph theory and combinatorics, CIRM – Marseille Luminy, France (July 12, 1990).
    156. “Supersolvable matroid extensions.” RISC-workshop on combinatorics and computational algebraic geometry, RISC – Linz, Austria (May 25, 1989).

University and Community Service

George Mason University

  • 2026 Course Coordinator for Math 214
  • 2026 Ph.D. Thesis Defense Committee, Chair (Justin Thorpe)
  • 2026 Ph.D. Thesis Defense Committee (Jessica Masterson)
  • 2025 Postdoctoral Research Fellow Search Committee, Chair
  • 2025 Ph.D. Thesis Defense Committee (Alonso Ogueda-Oliva)
  • 2025 Ph.D. Candidacy Exam Committee, Chair (Frank Pryor)
  • 2025 Ph.D. Candidacy Exam Committee (Sky Ratcliffe)
  • 2025 Habilitation Jury, École Polytechnique, France (Maxime Breden)
  • 2025 Ph.D. Thesis Defense Committee, Technische Universität München, Germany (David Hien)
  • 2025 Ph.D. Thesis Defense Committee (Biniyam Tibebu)
  • 2025 Ph.D. Candidacy Exam Committee (Nicholas Chisholm)
  • 2025 Ph.D. Candidacy Exam Committee (Allison Kohne)
  • 2025 Ph.D. Candidacy Exam Committee (Anthony Pizzimenti)
  • 2025 Graduate Student Faculty Mentor (Kelsi Listman)
  • 2025 Course Coordinator for Math 214
  • 2024–2025 College of Science Promotion and Tenure Committee, Secretary
  • 2024 Ph.D. Thesis Defense Committee (Patrick Bishop)
  • 2024 Ph.D. Candidacy Exam Committee (Jessica Masterson)
  • 2024 Graduate Student Faculty Mentor (Kelsi Listman)
  • 2024 Peer Reviewer for Teaching (T. Berry)
  • 2023–2024 College of Science Promotion and Tenure Committee, Secretary
  • 2023 Ph.D. Candidacy Exam Committee (Alonso Ogueda-Oliva)
  • 2023 Ph.D. Candidacy Exam Committee (Jessica Masterson)
  • 2023 Ph.D. Candidacy Exam Committee (Biniyam Tibebu)
  • 2023 Graduate Student Faculty Mentor (Kelsi Listman)
  • 2023 Peer Reviewer for Teaching (G. De La Pena)
  • 2022–2023 College of Science Promotion and Tenure Committee, Co-Secretary
  • 2022 M.S. Committee (Wafaa Mahzari)
  • 2022 Ph.D. Thesis Defense Committee, Chair (Peter Rizzi)
  • 2022 Ph.D. Thesis Defense Committee (Deanna Easley)
  • 2022 Ph.D. Candidacy Exam Committee (Patrick Bishop)
  • 2022 Peer Reviewer for Teaching (S. Bruschi, D. Eckley)
  • 2021 Ph.D. Candidacy Exam Committee, Chair (Justin Thorpe)
  • 2021 Graduate Student Faculty Mentor (Sameer Savkar)
  • 2021 Graduate Student Faculty Mentor (Jackson Williams)
  • 2021 Ph.D. Thesis Defense Committee, External Reviewer, Universidad Complutense de Madrid, Spain (Pedro Chocano)
  • 2021 M.S. Committee, Chair (Lauren Joyave)
  • 2021 Ph.D. Candidacy Exam Committee, Chair (Peter Rizzi)
  • 2020 Ph.D. Thesis Defense Committee (Sayomi Kamimoto)
  • 2020 Ph.D. Candidacy Exam Committee (Deanna Easley)
  • 2020 Ph.D. Thesis Defense Committee (Ryan Vaughn)
  • 2020 Ph.D. Candidacy Exam Committee, Chair (Justin Thorpe)
  • 2020 Ph.D. Thesis Defense Committee, External Member, University of Sherbrooke, Canada (Reza Ghamarshoushtari)
  • 2019 Ph.D. Thesis Examination Committee, External Member, University of Sherbrooke, Canada (Reza Ghamarshoushtari)
  • 2019 Ph.D. Candidacy Exam Committee (Sayomi Kamimoto)
  • 2019 Peer Reviewer for Teaching (K. Nong)
  • 2018 Ph.D. Candidacy Exam Committee (Ryan Vaughn)
  • 2017 Ph.D. Thesis Defense Committee (Diego Torrejon)
  • 2017 Ph.D. Candidacy Exam Committee (Ryan Vaughn)
  • 2017 Ph.D. Thesis Defense Committee, Chair (Patrick O’Neil)
  • 2017 M.S. Committee (Stephanie Mui)
  • 2017 Peer Reviewer for Teaching (H. Antil, S. Lawton)
  • 2016 Ph.D. Candidacy Exam Committee (Diego Torrejon)
  • 2016 Ph.D. Thesis Defense Committee (Hasitha de Silva)
  • 2016 Ph.D. Candidacy Exam Committee, Chair (Patrick O’Neil)
  • 2016 Peer Reviewer for Teaching (G. Agnarsson, H. Lamba)
  • 2016 Ph.D. Thesis Defense Committee, Chair (Thomas Stephens)
  • 2016 M.S. Committee (Zach Pryor)
  • 2014–2016 Departmental Policy & Hiring Committee
  • 2015 Ph.D. Thesis Defense Committee (Jonathan Lisic)
  • 2015 Peer Reviewer for Teaching (G. Agnarsson, H. Antil)
  • 2015 Peer Reviewer for Teaching (S. Schluchter, G. De La Pena, H. Razafinjatovo, D. Eckley, M. Holzer)
  • 2015 Ph.D. Candidacy Exam Committee, Chair (Patrick O’Neil)
  • 2015 Ph.D. Candidacy Exam Committee (Hasitha de Silva)
  • 2015 Ph.D. Candidacy Exam Committee (Diego Torrejon)
  • 2015 Ph.D. Candidacy Exam Committee, Chair (Thomas Stephens)
  • 2015 Ph.D. Candidacy Exam Committee (Jonathan Lisic)
  • 2012–2014 Departmental IT Manager
  • 2014 Peer Reviewer for Teaching (J. Boyette, G. Bulancea)
  • 2014 Ph.D. Candidacy Exam Committee (Alathea Jensen)
  • 2014 Ph.D. Candidacy Exam Committee, Chair (Thomas Stephens)
  • 2014 Ph.D. Thesis Defense Committee (Pin Ren)
  • 2014 M.S. Committee (Ericson Davis)
  • 2013 Undergraduate Honors Thesis Committee (Andy Zeng)
  • 2013 Ph.D. Candidacy Exam Committee (Hasitha de Silva)
  • 2013 Ph.D. Thesis Defense Committee (Maziar Raissi)
  • 2013 Peer Reviewer for Teaching (E. Addo, A. Goetz, C. Sausville)
  • 2013 Ph.D. Thesis Defense Committee (Tyrus Berry)
  • 2013 Ph.D. Candidacy Exam Committee (Maziar Raissi)
  • 2013 Ph.D. Candidacy Exam Committee (Pin Ren)
  • 2012 Ph.D. Candidacy Exam Committee (Jonathan Lisic)
  • 2011 Departmental Representative, COS Director of Technologies Hiring Committee
  • 2011 Ph.D. Thesis Defense Committee, Chair (Scott Cochran)
  • 2011 M.S. Committee, Chair (Mike Atkins)
  • 2011 Ph.D. Candidacy Exam Committee (Tyrus Berry)
  • 2010–2011 Director of the GMU Math URCM Program
  • 2008–2011 Ph.D. Candidacy Exam Committee (Robert Reznik)
  • 2010 Ph.D. Thesis Defense Committee (Richard Tatum)
  • 2010 Ph.D. Candidacy Exam Committee, Chair (Scott Cochran)
  • 2008–2010 Departmental Policy & Hiring Committee
  • 2007–2010 College of Science Promotion and Tenure Committee
  • 2009 Ph.D. Thesis Defense Committee (Javed Siddique)
  • 2009 Ph.D. Thesis Defense Committee, Co-Chair (Andrew Corrigan)
  • 2009 M.S. Committee (Terrance Flynn)
  • 2008 Departmental Endowed Professor Hiring Committee, Chair
  • 2008 M.S. Committee, Chair (Elan Rodan)
  • 2008 Ph.D. Candidacy Exam Committee (Richard Tatum)
  • 2008 Ph.D. Candidacy Exam Committee, Co-Chair (Andrew Corrigan)
  • 2008 Ph.D. Thesis Defense Committee, Chair (Tina Hartley)
  • 2006–2008 Departmental Graduate Committee
  • 2007 M.S. Committee (Mary Ann Graham)
  • 2007 Ph.D. Candidacy Exam Committee, Chair (Tina Hartley)
  • 2007 Ph.D. Candidacy Exam Committee (Javed Siddique)
  • 2005–2007 Departmental Colloquium Committee
  • 2006 Ph.D. Thesis Defense Committee (Timothy Seaman)
  • 2006 Preliminary Exam Committee (Linear Analysis, ODE)
  • 2006 Honors Thesis Committee (Tyler White)
  • 2003–2006 Departmental SCS Liaison
  • 2005 Ph.D. Candidacy Exam Committee (Timothy Seaman)
  • 2005 Departmental Postdoc Hiring Committee
  • 2005 Departmental Hiring Committee
  • 2003 M.S. Committee (Karen Crossin)
  • 2003 Undergraduate Grade Appeal Committee

University of Maryland, Baltimore County

  • 2005 Ph.D. Thesis Defense Committee (Valeriy Korostyshevskiy)
  • 2004 M.S. Thesis Defense Committee, Chair (Jonathan Desi)
  • 2003 Ph.D. Qualifying Exam Committee (Valeriy Korostyshevskiy)
  • 2002 Ph.D. Thesis Defense Committee (Devasis Bassu)
  • 2002 M.S. Thesis Defense Committee, Chair (Jennifer Deering)
  • 2001–2002 Applied Mathematics Colloquium Organizer
  • 2001–2002 Departmental Hiring Committee (Applied Mathematics)
  • 2001 Ph.D. Qualifying Exam Committee (Justin Nave)
  • 1998–2001 Departmental Graduate Program Committee
  • 2001 Ph.D. Thesis Defense Committee (Igor Shimansky)
  • 2001 Differential Equations Seminar Organizer
  • 2000–2001 Departmental Library Liaison
  • 1999–2000 Hiring Committee (Department Chair)
  • 1999–2000 Departmental Hiring Committee (Scientific Computing)
  • 1999 Ph.D. Qualifying Exam Committee (Devasis Bassu)
  • 1999 M.S. Thesis Defense Committee (Yoon Song)
  • 1998–1999 Classroom Instructional Technology Committee