Table of Contents Home Contact information Curriculum vitae Publications Henon computations CHomP ad Student research Teaching Links Email me			pdf version    Education Ph.D. (Mathematics) Georgia Institute of Technology, Summer 2003 A Rigorous Numerical Method in Infinite Dimensions , Ph.D. dissertation (or just the first 10 pages here .) M.S. (Mathematics) Emory University, Spring 1998 Chaotic Dynamics on Julia Sets for the Quadratic Family , M.S. dissertation B.S. (Mathematics/Physics) Emory University, Spring 1998 Presentations       Computer-assisted proofs for dynamical systems. Applied Mathematics Seminar, GWU, October 2009. Computer-assisted proofs for dynamical systems. joint CSUMS seminar talk with Rafael Frongillo, September 2008. Braids and connecting orbits in parabolic PDEs. William and Mary department colloquium, September 2008. Connecting orbits for parabolic PDEs via braid theory.  Computational Topology and Dynamics Workshop, MSU, Bozeman, August 2008. Symbolic dynamics via computational topology. Workshop on Computational Algebraic Topology, MFO (Oberwolfach), June/July 2008. Constructing symbolic dynamics representations via Conley Index theory. FoCM 2008, Hong Kong, June 2008. Computer-assisted proofs for the Kot-Schaffer model.  AMS Sectional meeting, Session on Mathematical Modeling in Biology, March 2008. Real Henon Maps -- Entropy.  Workshop on Computer-Assisted Nonlinear Dynamics (CANDY 08), Imperial College London, March 2008. Computer-assisted proofs for dynamical systems.  George Mason University, February 2008. Algorithms for symbolic dynamics and entropy bounds.  In a minisymposium on Computational Topology and Dynamics,  ICIAM 07, Zurich, July 2007. Validated continuation.  In a minisymposium on ``Numerical Bifurcation Analysis and Applications.''  SIAM Conference on Applications of Dynamical Systems, Snowbird, May/June 2007. Computer-assisted proofs in dynamical systems.  Wichita State University, April 2007. Computational tools for measuring topological entropy. AMS Southeastern Sectional Meeting, Davidson, March 2007. Computing symbolic dynamics and entropy for nonlinear systems. Rutgers University, November 2006. Dynamics I, II, and III.  seminar series at MSRI, September 2006. Computational topology in the study of dynamical systems.  Workshop on Applications of Topology in Science and Engineering, MSRI, September 2006. Topological methods for dynamical systems.  A mini-course in a workshop on Recent Developments in Arrangements and Configuration Spaces, MSRI,  August 2006. Validity of homology computations for nodal domains.  Workshop on Computational and topological aspects of dynamics, Leiden, May 2006. Computer-Assisted Proofs for Dynamical Systems.  College of William and Mary, February 2006. Computer-Assisted Proofs for Dynamical Systems:  from stationary solutions to global attractors.  Florida Atlantic University, February 2006. Continuation and Computer-Assisted Proofs:  a study of the Swift-Hohenberg system.  Vrije Universiteit, Amsterdam, January 2006. Computer-Assisted Proofs in Dynamics:  from fixed points to chaos.  Stony Brook University, December 2005. Computing the Homology of Relative Braid Classes: algorithms and implications.  Université de Sherbrooke, November 2005. Continuation and Computer-Assisted Proofs:  a study of the Swift-Hohenberg equation.  Université de Montréal, November 2005. Homology Computations on Braid Classes:  algorithms and implications.  Georgia Tech, October 2005. Rigorous continuation techniques.  George Mason University, October 2005. Continuation and Computer-Assisted Proofs:  a study of the Swift-Hohenberg equation.  CAM Colloquium, Cornell University, September 2005. A topological approach for numerical studies of infinite-dimensional maps.  Invited talk, Third Pacific Rim Conference on Mathematics, Shanghai, August 2005. Computer-Assisted Proofs in Dynamics:  from fixed points to chaos.  Smorgasbord talk, Cornell University, June 2005. Dimension reduction techniques for rigorous numerics.  SIAM Conference on Applications of Dynamical Systems, Snowbird, May 2005. Constructing models of global attractors for Swift-Hohenberg.  SIAM Conference on Applications of Dynamical Systems, Snowbird, May 2005. Computer-assisted proofs for dynamical systems.  Oliver Club, Cornell University, April 2005. Rigorous Computations: detecting chaos and rejecting spurious solutions. Workshop on Qualitative Numerical Analysis of High-Dimensional Nonlinear Systems, Bristol, March 2005. A numerical approach to constructing models for global attractors.  Pan-American Advanced Studies Institute 2005, Santiago, January 2005. A multivalued approach to time series analysis.  Osaka University, December 2004. Rigorous numerics for infinite dimensional dynamical systems. University of Minnesota, November 2004. Rigorous numerics and the Henon map.  Summer School on the Conley Index and Computational Homology.  Pappenheim, Germany, September 2004. Rigorous numerics based on the Conley index:  infinite-dimensional maps.  Dynamical Systems Seminar, Cornell University, September 2004. Rigorous numerics for global dynamics.  International Conference on Nonlinear Dynamics and Evolution Equations.  Memorial University of Newfoundland,  July 2004. Conley index techniques for global dynamics: a study of the Swift-Hohenberg equation.  Max Planck Institute, Leipzig, June 2004. Conley index techniques for global dynamics: a study of the Swift-Hohenberg equation.  Free University, Berlin, June 2004. Rigorous numerical methods based on the Conley index:  a finite-dimensional example.  US-Japan workshop on Dynamics and Computations, Tokyo, March 2004. Conley index techniques in numerical studies of finite dimensional systems.  invited lecture series, Osaka University, February 2004. Numerics and the Conley index: GAIO, CHomP, and two examples. CWI, Amsterdam, November 2003. Index techniques and bifurcation diagrams, University of Paderborn, November 2003. A rigorous numerical method in infinite dimensions, Vrije Universiteit, Amsterdam, October 2003. Chaotic Symbolic Dynamics in the Kot-Schaffer Model, Butler conference, Edmonton, June 2003. Regularity Properties of Infinite Dimensional Systems and a Rigorous Numerical Method, NDDS, Kyoto, August 2002. Low Dimensional Objects in High Dimensional Systems, MWDS, UNCA, April 2002. A Rigorous Numerical Method for the Analysis of an Infinite Dimensional Discrete Dynamical System, AMS and MAA Spring Southeastern Section Meetings, Atlanta, March 2002. Low Dimensional Objects in Infinite Dimensional Systems , Workshop on Low Dimensional Dynamics, University of Florida, November 2001. A Rigorous Numerical Method for the Global Analysis of an Infinite Dimensional Discrete Dynamical System , University of Paderborn, April 2001. Conferences    and Workshops Computational Topology and Dynamics Workshop.  MSU, Bozeman, August 2008. Workshop on Rhythms in the Hypothalamus and Pituitary.  AIM, Palo Alto, August 2008. Workshop on Computational Algebraic Topology.  MFO (Oberwolfach), June/July 2008. FoCM 2008.  Hong Kong, June 2008. Session on Mathematical Modeling in Biology, AMS Sectional meeting.  March 2008. Workshop on Computer-Assisted Nonlinear Dynamics (CANDY 08).  Imperial College London, March 2008. ICIAM 07.  Zurich, July 2007. SIAM Conference on Applications of Dynamical Systems.  Snowbird, May/June 2007. Special Session on Dynamical Systems, AMS Southeastern Sectional Meeting. Davidson, March 2007. Workshop on Computational Applications of Algebraic Topology.  semester workshop at MSRI, Fall 2006. Workshop on computational and topological aspects of dynamics.  Lorentz Center, Leiden, May 2006. Third Pacific Rim Conference on Mathematics.  Fudan University, Shanghai, August 2005. SIAM Conference on Applications of Dynamical Systems.  Snowbird, May 2005. Workshop on Qualitative Numerical Analysis of High-Dimensional Nonlinear Systems.  University of Bristol, March 2005. Pan-American Advanced Studies Institute 2005.  Santiago, Chile, January 2005. Summer School on the Conley Index and Computational Homology.  Pappenheim, Germany, September 2004. International Conference on Nonlinear Dynamics and Evolution Equations.  Memorial University of Newfoundland,  July 2004. US-Japan workshop on Dynamics and Computations, Shonan International Center, Tokyo, March 2004. Kyoto Dynamics Days 3, Kyoto University, March 2004. Fourth Butler Memorial Conference, University of Alberta, June 2003. New Directions in Dynamical Systems, (Kyoto, Japan), August 2002. Midwest Dynamical Systems (MWDS) Conference University of North Carolina at Asheville, April 2002. AMS and MAA Spring Southeastern Section Meetings Atlanta, Georgia, March 2002. Workshops on Low Dimensional Dynamics and Applications of Dynamics, University of Florida, November 2001. Second Workshop on the Conley Index and Related Topics, Université de  Sherbrooke, August 2001. Midwest Dynamical Systems Seminar, 30th Anniversary Conference, University of Cincinnati, September 2000. European Sociey for Mathematical and Theoretical Biology (ESMTB) Summer School (Martina Franca, Italy), September 2000. IMA Summer Program for Graduate Students on "Dynamical Systems and Applications," Pennsylvania State University, June 1999.