Welcome to Zheng Gan's Home Page
Ph.D in Mathematics
Advisor : Professor David Damanik
Office: Basement 14, Herman Brown
E-mail: [my first name].[my last name] (at) rice.edu
Mailing Address: Math Department - MS 136,
Rice University, 6100 S. Main St., Houston, TX 77005.
Hometown: Huzhou city ( it is known as the "Land of Fish and Rice" ), Zhejiang province, China
- Rice University, Houston, U.S.A., PhD, Sept. 2007 --- May. 2012
- Univ. of Science and Technology of China, Hefei, China, B.S., Sept. 2003 --- June 2007
- Huzhou High School, Huzhou, China, Sept. 2000 --- June 2003
Research Interests: Spectral Theory of Schrödinger Operators; Quantum Dynamics
I am interested in limit-periodic Schrödinger operators, which can be regarded as generated by continuous sampling
along the orbits of a minimal translation of a Cantor group. Within this frame, I am studying some basic and important roles in quantum dynamics,
like Lyapunov exponents, integrated densities of states, spectrum types (a.c.,s.c. & p.) and etc.
- A Remark on the Hull of a Multi-Dimensional Limit-periodic Potential, to appear in Mathematical Modelling of Natural Phenomena, [PDF]
- Limit-Periodic Schrödinger Operators on Z^d:
Uniform Localization (with David Damanik), preprint, [PDF]
- Discontinuity of the Lyapunov Exponent (with H. Krüger), preprint, [PDF]
- Limit-Periodic Schrödinger Operators with Uniformly Localized Eigenfunctions (with D. Damanik), Journal d'Analyse Mathematique,
115, 33-49 (2011)[PDF]
- An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups,
Mathematical Modelling of Natural Phenomena, 5:4, 158-174 (2010) [PDF]
- Limit-Periodic Schrödinger Operators in the Regime of Positive Lyapunov Exponents (with D. Damanik), Journal of Functional Analysis,
258:12, 4010-4025 (2010) [PDF]
- Optimality of log Hölder Continuity of the Integrated Density of States (with H. Krüger),
Mathematische Nachrichten, 284:14-15, 1919-1923 (2011) [PDF]
- Spectral Properties of Limit-Periodic Schrödinger Operators (with D. Damanik), Communications on Applied and Pure Mathematics,
10, 859-871 (2011) [PDF]
What are mathematicians doing?
Many people don't understand what mathematicians are doing, since math hasn't direct influence to our society.
It is my pleasure to recommend an artical written by William Thurson, the fields medal winner, introducing you to the world of mathematicians.
Please refer to arXiv:math/9404236.
Some Web-page Links
This page was last modified May 16, 2012.