School of Mathematics
University of Minnesota
206 Church St. SE
Minneapolis, MN 55455
Office: Vincent Hall 531
I am a Postdoctoral Associate in the School of Mathematics and the Simons Collaboration on Localization of Waves at the University of Minnesota, working with Svitlana Mayboroda. I earned my Ph.D. in Mathematics at UC, Irvine in June 2016 under my dissertation advisor: Svetlana Jitomirskaya. Here is my curriculum vitae: CV
Mathematical Physics, Spectral Theory, Dynamical Systems, Harmonic Analysis, Partial Differential Equations
I am also interested in working with undergraduate students on projects that are related to my research. If you are currently UMN undergraduate students who wish to participate in research projects, feel free to contact with me. Here is the recent undergraduate research project on Landscape Theory that I instructed (together with Ilya Kachkovskiy) at the Michigan State University in spring 2019.
Education & Employment:
- 2019-present: Postdoctoral Associate, School of Mathematics & Simons Collaboration on Localization of Waves, University of Minnesota
- 2016-2019: Visiting Assistant Professor, Department of Mathematics at the Michigan State University.
- 2013-2016: Ph.D. Mathematics, University of California, Irvine — Irvine, CA
- 2009-2013: graduate student in Mathematics, Nanjing University, China. (Transfer to UC Irvine in Sept. 2013)
- 2005-2009: B.S. Mathematics, Nanjing University, China.
- I. Chenn, S. Mayboroda, W. Wang, and S. Zhang. On a Novel Effective Equation of the
Reduced Hartree-Fock Theory with Random Potential. In preparation.
- I. Chenn, W. Wang, and S. Zhang, Approximating the Ground State Eigenvalue via the Landscape Potential. In preparation.
- D. N. Arnold, S. Mayboroda, W. Wang and S. Zhang, Numerical analysis on the practical landscape law. In preparation.
- I. Chenn, S. Zhang. On the Reduced Hartree-Fock Equation with Anderson Type Background Charge
- D. N. Arnold, M. Filoche, S. Mayboroda, W. Wang and S. Zhang, The landscape law for tight binding Hamiltonians. arXiv:2101.03282. submitted.
- P. Desforges, S. Mayboroda, S. Zhang, G. David, D. N. Arnold, W. Wang, and M. Filoche. Sharp estimates for the integrated density of states in Anderson tight-binding models. arXiv:2010.09287. submitted.
- S. Jitomirskaya, S. Zhang, Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators. arXiv:1510.07086. To appear in J. Eur. Math. Soc.
- R. Han, F. Yang and S. Zhang, Spectral dimension for β-almost periodic singular Jacobi operators and the extended Harper's model. To appear in Journal d'Analyse Mathématique.
- W. Wang, S. Zhang, The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions, To appear in Ann. Henri Poincaré.
- J. Schenker, Z. Tilocco and S. Zhang, Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential. Commun. Math. Phys., 377, 1597-1635 (2020).
- S. Jitomirskaya, W. Liu and S. Zhang, Arithmetic spectral transitions: a competition between hyperbolicity and the arithmetics of small denominators. (Lecture Notes.) To appear in IAS/Park City Mathematics Series: Harmonic Analysis, 2018.
- F. Yang, S. Zhang, Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schrödinger operators. Ann. Henri Poincaré 20: 2481 (2019).
- S. Zhang, The exact power law for Buffon's needle landing near some random Cantor sets. Revista Matemática Iberoamericana, Vol.36 (2), p.537-548 (2020).
- R. Han, S. Zhang, Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles. Int. Math. Res. Not., rnz319, (2019).
- S. Zhang, Mixed spectral types for one frequency discrete quasi-periodic Schrödinger operator. Proc. Amer. Math. Soc. 144 (2016), 2603-2609.
- J. You, S. Zhang and Q. Zhou, Point Spectrum of the Quasi-Periodic Long
Range Operators. J. Spectr. Theory 4 (2014), 769-781.
- J. You and S. Zhang, Hölder continuity of the Lyapunov exponent for
analytic quasiperiodic Schrödinger cocycle with
weak Liouville frequency. Ergodic Theory Dynam. Systems 34 (2014), 1395-1408.
- S. Zhang, Z. Zhao, Diffusion Bound and Reducibility for Discrete Schrödinger Equations with Tangent Potential. Front. Math. China 7 (2012), 1213-1235
Recent Conferences & Seminars:
Organizer: (together with Ilya Kachkovskiy and Matthew Cha), AMS Fall Central Sectional Meeting 2018, Special Session "Ergodic and topological quantum systems", Ann Arbor, October 20-21, 2018.
- Math Physics Seminar Talk, UCI, CA, Nov 15, 2019
- Probability Seminar Talk, UCLA, CA, Nov 14, 2019
- Analysis Seminar Talk, Yale University, CT, Spetember 28, 2018
- Dynamical Systems Seminar Talk, Tsinghua University, China, May 23, 2018
- Ergodic Theory and Spectral Theory Seminar Talk, UCR, May 18, 2018
- Dynamical Systems Seminar Talk, MSU, March 1, 2018.
- Dynamical Systems Seminar Talk, Nanjing University, Nanjing, China. July 27, 2017.
- Analysis and PDE Seminar Talk, MSU. Oct 31, 2016.
- Dynamical Systems and Fractal Geometry Seminar Talk, Mathematics Morningside center, CAS, Beijing, China. May 22, 2015
- Dynamical Systems Seminar Talk, Nanjing University, Nanjing, China. July 20, 2014.
- Geometry-Analysis Seminar Talk, Rice University, Houston, Texas. April 23, 2014.
Conferences & Workshops:
- Proposed mini-course speaker for the proposed Summer School on Periodic and Ergodic Spectral Problems, to be held Summer 2021 in Montreal.
- (canceled) NSF-CBMS Regional Research Conferences, Florida State University, Aug 17-21, 2020
- (canceled) New directions in disordered systems-on the occasion of the 75th birthday of Abel Klein, the Institute of Advanced Studies of CY Cergy Paris Université, France, June 28-July 3, 2020
- (canceled) Almost-Periodic Spectral Problems, Banff International Research Station, Canada, April 12-17, 2020
- Simons Collaboration on Localization of Waves Annual Meeting, New York, NY, Feb 20-21, 2020
- Joint Mathematics Meetings AMS Special Session on Localization and Delocalization for Disordered Quantum Systems, Baltimore Convention Center, January 18-19, 2019.
- Spectral Theory of Quasi-Periodic and Random Operators, CRM, Montreal, November 12-16, 2018.
- Recent Advances in Functional Analysis-dedicated to the memory of Joe Diestel and Victor Lomonosov, poster session, Kent State University, October 11-14, 2018.
- Young Researchers Symposium at ICMP, McGill University, Montreal 07/21/2018
- 28th Annual PCMI Summer Session: Research Program in Harmonic Analysis, Park City, Utah, July 1 – July 21, 2018.
- Special Session on ``Spectral Theory'' at the AMS sectional meeting, Portland, OR, April 14-15, 2018
- 8th Ohio River Analysis Meeting, University of Kentucky, Lexington, March 24-25, 2018
- Special Session on Spectral Theory, Disorder and Quantum Physics at the JMM, San Diego, CA, Jan 10-13, 2018
- Recent Developments in Harmonic Analysis, MSRI, Berkeley, CA 05/15-05/19/2017
- 7th Ohio River Analysis Meeting, University of Cincinnati 03/25/2017
- Introductory Workshop: Harmonic Analysis, MSRI, Berkeley, CA 01/23-01/27/2017
- AMS Special Session at the Joint Mathematics Meeting, Seattle, WA, Jan 6-9, 2016
- AMS Fall Western Sectional Meeting, Fullerton, CA, Oct 24-25, 2015
- Workshop: Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory, BIRS, Oaxaca, Mexico, Sept 27-Oct 2, 2015
- Almost Periodic and Other Ergodic Problems, University of Cambridge, UK, Mar 20-May 20, 2015
- 33nd Annual Western States Mathematical Physics Meeting, Caltech, Pasadena, CA, Feb 16-17, 2015
- Special Session at the USA-Uzbekistan Conference on Analysis and Mathematical Physics, CSUF, Fullerton ,CA, May 20-24, 2014
Teaching/General audience Talks:
- Math. Department Colloquium, Oberlin College, Oberlin, OH. 09/20/2018
- Department Seminar, Loyola Marymount University, Los Angeles, CA. Nov 5, 2015
- Colloquium at CSULB, Long Beach, CA. Mar 13, 2015
- Geometry and Topology Seminar, CSUF, Fullerton, CA. Feb 20, 2015
- Kovalevsky Outstanding PhD Thesis Award, UC Irvine 2016
- Euler Award for Outstanding Promise as a Graduate Student, UC Irvine 2014
- Samsung Scholarship, Nanjing University, China 2007
- National Encouragement Scholarship, Nanjing University, China 2006
Current Teaching at University at Minnesota:
MATH 4512, Differential Equations with Applications, Spring 2021.
Math 1271, Calculus I, Fall 2020.
Math 1271, Calculus I, Fall 2019. Class Webpage.
Past Teaching at MSU:
- Undergrad Rsearch Program at MSU (part of the Discovering America Program of math department at MSU) on Landscape theory, Fall 2018, Spring 2019. Project website.
- Teaching Assistant for lectures by Svetlana Jitomirskaya at the PCMI Graduate Summer School on Harmonic Analysis, Park City, July 2018: Arithmetic spectral transitions: a competition between hyperbolicity and the arithmetics of small denominators, July 8–14, 2018
Past Teaching at UCI:
- Winter 2015, UC Irvine: TA Math 3D, Elementary Differential Equation.
- Fall 2015, UC Irvine: Instructor for Math 2B, Calculus II. Course Webpage
- Summer 2015, UC Irvine: TA
Math 176/Econ135: Math of Finance (Summer Session II, 2015)
Fall 2014, UC Irvine: TA Math 2B: Calculus II