My research is motivated by the rapid expansion of model complexity and data availability in the applied sciences. Traditional parametric modeling is subject to model error and I believe that modern complex systems call for model-free and semi-parametric approaches. In order to avoid the curse-of-dimensionality, these approaches must effectively incorporate available prior knowledge and existing models. My goal is to develop these techniques with careful consideration of the goals and constraints of real world case studies.
Geometry of data: diffusion maps/local kernels, nonlinear dimensionality reduction and decomposition
Statistics: kernel density/operator estimation, semi-parametric modeling of dynamical systems
Dynamical systems: data assimilation, prediction/control, and uncertainty quantification
Harmonic analysis: Sampling theory on manifolds, connections to kernel based statistical estimates
2015 AMMCS-CAIMS Congress - Wilfrid Laurier University, June 11, 2015. (slides)
Courant Institute Applied Math Seminar, March 13, 2015. (slides)
George Mason University Applied Math Seminar, February 27, 2015. (slides)
2014 SIAM Conference on Uncertainty Quantification, Savannah, GA, April 1, 2014. (program)
ONR-MURI Workshop, Courant Institute, January 20-22, 2014. (slides)
4th Annual Joint PSU-UMD Data Assimilation Workshop, Pennsylvania State University, Dec. 18, 2013. (slides)
WMO Sixth Symposium on Data Assimilation, University of Maryland, College Park, October 7-11, 2013. (poster)
2013 Interdisciplinary Summer School: Data Assimilation in Geosciences, University of Maryland, College Park, June 3-14, 2013. (slides (revised), original)
Snowbird SIAM Conference on Applications of Dynamical Systems, May 19-23, 2013. (Presentation)
IMA Annual Program Year Workshop: Stochastic Modeling of the Oceans and Atmosphere, University of Minnesota, Twin Cities Campus, March 11-15, 2013. (poster)
Building Engineered Complex Systems Workshop, Jan. 24-25, 2013 (poster)
Joint Mathematics Meeting at Boston, January 4, 2012 at 9:30, Special Session for Difference Equations and Applications, I. (abstract)
Snowbird SIAM Conference on Applications of Dynamical Systems, May 22-26, 2011 (poster)
Building Engineered Complex Systems Workshop, Mar. 28-29, 2011 (poster)
February Fourier Talks, University of Maryland, Feb. 17 - 18, 2011 (poster)
AMS Meeting at Syracuse University, October 2, 2010, Special Session on Difference Equations and Applications. (schedule, abstract)