Marzuola, Jeremy L
I study a variety of partial differential equation and probabilistic models arising in various settings such as fluid dynamics, material science, statistical and optical physics and quantum mechanics.
B.A. University of Oklahoma, 2002; Ph.D., University of California, Berkeley, 2007; National Science Foundation Postdoctoral Fellow at Columbia University, 2007-2008, 2009-2010; Hausdorff Center Postdoc at Universität Bonn, 2008-09.
My research interests include soliton and vortex existence/stability, well-posedness theory for quasilinear and degenerate models, linear scattering theory, spectral theory, Strichartz/dispersive estimates, microlocal analysis, properties of eigenfunctions on billiards, classical dynamics descriptions of Analysis & PDEs solutions, graph Laplacian spectral problems, spectral theory of combinatorial and quantum graphs, numerical simulations, asymptotic analysis, degenerate dispersive/diffusive equations with applications in nonlinear optics, fluid dynamics, topological physics, material science, quantum mechanics, general relativity, quantum chemistry, statistical physics, and weak turbulence.
Nodal Deficiency, Spectral Flow, and the Dirichlet-To-Neumann Map
Gregory Berkolaiko, Graham Cox, Jeremy L. Marzuola,
Letters in Mathematical Physics, 109, 1611-1623, 2019
The Relaxation of A General Family of Broken Bond Crystal Surface Models
Jeremy L. Marzuola, Jonathan Weare,
Physical Review E, 88, 032403, 2013
Quasilinear Schrödinger Equations I: Small Data and Quadratic interactions
Jeremy L. Marzuola, Jason Metcalfe, Daniel Tataru,
Advances in Mathematics, 231, 2, 1151-1172, 2012