Curriculum Vitae

Chongchun Zeng

 

Education

 

Professional Experience

  • September 2009 -- present: Professor, School of Math., Georgia Institute of Technology
  • September 2005 -- August 2009: Associate Professor, School of Math., Georgia Institute of Technology
  • September 2000 -- August 2005: Assistant Professor, Dept. of Math., University of Virginia
  • September 1997 -- August 2000: Courant Instructor, Courant Institute of Math. Sci., New York University

 

Research Grants and Awards

  • Interface problems in fluids and nonlinear waves. NSF DMS 0801319.
  • Sloan Fellowship: 2004.
  • Career Award: Career: Perturbation problems in PDE Dynamics. NSF DMS Analysis 0627842 (formerly 0239389), 2003-2008.
  • Hamiltonian motions under strong constraints. NSF DMS Analysis, 0101969, 2001-2004.
  • Dynamics of Weak Diffusive PDEs, New York University Research Challenge Fund, 1999, Awarded. (The proposal was externally reviewed.)

 

Research Interests : Applied dynamical systems and nonlinear PDEs

  • Free boundary problems in fluid mechanics, water waves.
  • Geometric Hamiltonian PDEs and their applications, such as wave maps and Schr\"odiner maps and etc., including (1) gauge transformations and blow-up related problems and (2) these PDEs with strong constraining potentials, their convergence to singular limits in various scales, averaging, dynamical structures, multi-scale analysis, and etc.;
  • General theory of infinite dimensional dynamical systems, including persistence, smoothness, and dynamics in neighborhoods, of invariant manifolds and foliations for semiflows, approximate invariant manifolds and their applications to PDE singular perturbations problems;
  • Dynamics of conservative PDEs under dissipative/conservative perturbations (unbounded/bounded), including quasi-periodic and homoclinic orbits for nonlinear wave and nonlinear Schr\"odinger equations

Selected Papers

  1. Existence and Persistence of Invariant Manifolds for Semiflows in Banach Spaces, Mem. Amer. Math. Soc., 645 (1998), 129 pp. (with P. Bates and K. Lu). (This paper received a FEATURED REVIEW from Math. Review.)
  2. Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., 52 (1999), 983-1046 (with P. Bates and K. Lu).
  3. Homoclinic orbits for perturbed sine-Gordon equation, Comm. Pure. Appl. Math., 53 (2000), 283-299 (with J. Shatah).
  4. Invariant foliations near a normally hyperbolic invariant manifold for semiflows, Trans. Amer. Math. Soc., 352 (2000), 4641-4676 (with P. Bates and K. Lu).
  5. Homoclinic orbits for perturbed nonlinear Shroedinger equation, Comm. Pure. Appl. Math., 53 (2000), 1222-1283. (Erratum: Comm. Pure. Appl. Math., 53 (2000), 1603-1605.)
  6. Periodic solutions for Hamiltonian Systems under strong constraining forces, J. Diff. Equa. , 186 (2002), 572-585 (with J. Shatah).
  7. Orbits homoclinic to center manifolds of conservative PDEs, 24pp, Nonlinearity, 16 (2003), 591--614 (with J. Shatah).
  8. Constrained wave equations and wave maps, Comm. Math. Phys., 239 (2003), 383-404 (with J. Shatah).
  9. Schrodinger Maps and Anti-ferromagnetic Chains, Comm. Math. Phys., 262 (2006), 299-315 (with J. Shatah).
  10. Schroedinger Maps and their associated Frame Systems, IMRN, 2007 (2007) (with A. Nahmod, L. Vega, and J. Shatah). 
  11. Geometry and a priori estimates for free boundary problems of the Euler's equation, Comm. Pure. Appl. Math., 61 (2008), 698--744. (With J. Shatah.) 
  12. A priori estimates for fluid Interface problems, Comm. Pure. Appl. Math., 61 (2008), 848--876 (With J. Shatah).
  13. Approximately invariant manifolds and global dynamics of spike states, Inventiones Mathematicae, 174 (2008), 355--433. (With P. Bates and K. Lu.)
  14. Self-similar Solutions of Schr\"{o}dinger Flows, Calc. Var. Partial Differential Equations 34 (2009), 267--277. (With W. Ding and H. Tang.)
  15. Self-similar Solutions for the Schr\"{o}dinger map equation, to appear in Math. Z. (With P. Germain and J. Shatah.)