Michael I. Weinstein

PROFESSOR OF APPLIED MATHEMATICS AND PROFESSOR OF MATHEMATICS

212 S.W. Mudd
Mail Code 4701
http://www.columbia.edu/~miw2103/

Tel(212) 854-3624
Fax(212) 854-8257

Michael I. Weinstein works on the mathematical modeling, analysis, and applications of wave phenomena across many areas of physical science. A recent focus has been on PDE (Partial Differential Equations) models which describe optical and quantum waves in novel media such as topological insulators and metamaterials. Such physical media have applications to technologies which could potentially revolutionize robust information transfer in computing and communication systems.

Research Interests

Applied and fundamental mathematics, and the study of multi-scale wave phenomena.

Weinstein received a BSc in Mathematics from Union College, summa cum laude, in 1977 and a PhD in Mathematics from the Courant Institute at NYU in 1982. He is a Professor of Applied Mathematics in the Department of Applied Physics and Applied Mathematics and a Professor of Mathematics in the Department of Mathematics at Columbia University.  Weinstein is a Fellow of the American Mathematical Society (AMS) and a Fellow of the Society for Industrial and Applied Mathematics (SIAM). In 2015, he received a Math + X Investigator Award from the Simons Foundation.

PROFESSIONAL EXPERIENCE

  • Professor of Mathematics, Columbia University, 2014-present
  • Professor of Applied Mathematics, SEAS, Columbia University 2004-present,
  • MTS-Fundamental Mathematics Research Department, Bell Laboratories, Lucent Technologies, 1998-2004
  • Professor of Mathematics, University of Michigan, Ann Arbor, 1993-2000
  • Associate Professor of Mathematics (tenured) University of Michigan, Ann Arbor, 1988-1993
  • Assistant Professor of Mathematics, Princeton University, 1984-1988
  • NSF Postdoctoral Fellow, Stanford University, 1982-1984

HONORS & AWARDS

  • Simons Foundation Math + X Investigator Award, 2015-2020
  • Fellow of the AMS, 2014
  • SIAM Fellow, 2010

SELECTED PUBLICATIONS

  • Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature, (with A.B. Watson and J. Lu), Journal of Mathematical 58, 021503 Physics (2017)
  • Honeycomb Schroedinger operators in the strong binding regime, (with C.L. Fefferman and J.P. Lee-Thorp), Communications on Pure and Applied Mathematics, to appear - https://arxiv.org/abs/1610.04930
  • Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier (with M. Jenkinson), Communications in Mathematical Physics (2017)
  • Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures (with C.L. Fefferman and J.P. Lee-Thorp), 2D Materials, Volume 3 (2016)
  • Edge states in honeycomb structures (with C.L. Fefferman and J.P. Lee-Thorp),
  • Annals of PDE (2016) 2:12
  • Photonic realization of topologically protected bound states in domain-wall modulated waveguide arrays (with J. P. Lee-Thorp, I. Vukicevic, X. Xu, J. Yang, C. L. Fefferman and C. W. Wong ), Phys. Rev. A 93 (2016) 033822
  • Localized states and their dynamics in the nonlinear Schroedinger / Gross Pitaevskii equation, Frontiers in Applied Dynamics: Reviews and Tutorials, Volume 3, Springer (2015)
  • Scattering and localization properties of highly oscillatory potentials (with V. Duchene and I. Vukicevic), Commun. Pure Applied Math, Volume 67 (2014)
  • On-site and off-site solitary waves of the discrete nonlinear Schroedinger equation in multiple dimensions (with M. Jenkinson), Nonlinearity Volume 29, Number 1 (2016)
  • Topologically protected states in one-dimensional continuous systems and Dirac points (with C.L. Fefferman and J.P. Lee-Thorp) Proceedings of the National Academy of Sciences (2014), http://www.pnas.org/content/111/24/8759.full