Department of Mathematics

California Institute of Technology

Mail Code 253-37

Pasadena, California, 91125

U.S.A.

Email Address: gzhouXXXXX@caltechXX.edu, please remove the Xs'.

Mathematical Physics, Geometric Analysis, Nonlinear Partial Differential Equations

Research Statement: PDF

NSF DMS 1308985 and 1443225, Title: Quantum Friction, Resonance Problems and New Methods in Geometric Flows,

Requested amount $97,933, Period 2013-2017, Status: awarded.

(1)Ordinary differential equations in Caltech, fall 2016, large class of 237 students;

(2)Practical track of ordinary differential equations in Caltech, fall 2015, large class of 198 students;

(3)Discrete mathematics in the University of Illinois in Urbana Champaign, spring 2013, two sessions with about 60 students in total;

Other (smaller or earlier) classes: introduction to dynamical systems, introduction to mathematical chaos, methods in mathematical physics, scattering theory, new methods in geometric flows, partial differential equations

(1)Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann Equations,

(2)An unified approach in studying neckpinching of mean curvature flow,

(3)With Rupert Frank, an adiabatic theory for polaron.

(1) Zhou Gang, Perturbation expansion and N-order Fermi Golden rule, Journal of Mathematical Physics, 48(5):053509, 23, 2007.

(2) Zhou Gang and I.M.Sigal Soliton dynamics of nonlinear Schroedinger equations, Geometric and Functional Analysis, 116(6):1377--1390, 2006.

(3) Zhou Gang and I.M.Sigal, Asymptotic Stability of Nonlinear Schroedinger Equations with Potential, Reviews in Mathematical Physics, 17(10):1143--1207, 2005.

(4) S. Dejak, Zhou Gang, I.M.Sigal and S. Wang, Blow-up Problem of Nonlinear Heat Equations, Advances in Applied Mathematics, 40 (2008), no. 4, 433--481.

(5) Zhou Gang and I.M.Sigal, Relaxation To Trapped Solitons in Nonlinear Schroedinger Equations with Potential, Advances in Mathematics, 216(2):443--490, 2007.

(6) Zhou Gang and I.M.Sigal, Neck Pinching Dynamics Under Mean Curvature Flow, Journal of Geometric Analysis, 19 (2009), no. 1, 36--80

(7) Zhou Gang and Michael Weinstein, Dynamics of Nonlinear Schroedinger/Gross-Pitaevskii Equations; Mass Transfer in Systems with Solitons and Degenerate Neutral Modes, Analysis and PDE, 1 (2008), no. 3, 267--322.

(8) Zhou Gang and Michael Weinstein: Equipartition of Energy of nonlinear Schroedinger equations, Applied Mathematics Research Express, AMRX 2011, no. 2, 123-181.

(9) Juerg Froehlich, Zhou Gang and Avy Soffer: Some Hamiltonian Models of Friction, Journal of Mathematical Physics, 52, 083508 (2011). Selected for September 2011 issue of Virtual Journal of Atomic Quantum Fluids.

(10) Juerg Froehlich and Zhou Gang: Exponential Convergence to the Maxwell Distribution For Some Class of Boltzmann Equations, Communications in Mathematical Physics, Volume 314, Issue 2, pp 525-554.

(11) D.Knopf, Zhou Gang and I.M.Sigal: Neckpinching Dynamics of Asymmetric Surface Evolving by Mean Curvature Flow, to appear in Memoirs of the American Mathematical Society & arXiv:1109.0939v1

(12) Daniel Egli and Zhou Gang: Some Hamiltonian Models of Friction II, Journal of Mathematical Physics, 53, 103707 (2012)

(13) Juerg Froehlich, Zhou Gang and Avy Soffer: Friction in a Model of Hamiltonian Dynamics, Communcations in Mathematical Physics, Volume 315, Issue 2, pp 401-444

(14) Juerg Froehlich and Zhou Gang: On the theory of slowing down gracefully, Pramana, Journal of Physics, Vol. 78, No. 6, June 2012, pp 865-874

(15) Daniel Egli, Juerg Froehlich, Zhou Gang, Arick Shao and Israel Michael Sigal: Hamiltonian dynamics of a particle interacting with a wave field, Communication in Partial Differential Equations, Volume 38, Issue 12, 2013, Page 2155-2198

(16) Juerg Froehlich and Zhou Gang: Ballistic Motion of a Tracer Particle Coupled to a Bose gas, Advances in Mathematics, 259C (2014), pp. 252-268

(17) D.Knopf and Zhou Gang: Universality in mean curvature flow neckpinches, Duke Math. J. 164 (2015), no. 12, 2341-2406.

(18) Juerg Froehlich and Zhou Gang: Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction, Advances in Mathematics, 264, Oct 2014.

(19) Zhou Gang: A Resonance Problem in Relaxation of Ground States of Nonlinear Schroedinger Equations, arXiv:1505.01107.

(20) Rupert Frank and Zhou Gang: Derivation of an effective evolution equation for a strongly coupled polaron, to appear in Analysis & PDE.

(21) Thomas Farrell, Zhou Gang, Dan Knopf, Pedro Ontaneda: Sphere Bundles with 1/4-pinched Fiberwise Metrics, to appear in Transactions of American Mathematical Society.

(22) Zhou Gang, Philip Grech: An Adiabatic Theorem for the Gross-Pitaevskii Equation, Communications in Partial Differential Equations (accepted under the condition of revision), arXiv:1508.02351.