# Marzuola, Jeremy L

## Research Interests

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.

## Professional background

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.

## Research Synopsis

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.

## Representative Publications

*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