Shiwen Zhang

Assistant Professor

Department of Mathematical Sciences
UMass Lowell
Southwick Hall
11 University Ave.
Lowell, MA 01854

Office: Southwick Hall 304C (temp)
Email: shiwen_zhang@uml.edu

I am an Assistant Professor at the Department of Mathematical Sciences at UMass Lowell. Previously, I was a Postdoctoral Associate at University of Minnesota and Michigan State University. 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

Current Teaching:

Math 1290. Cal 1B. course website

Research Interests:

Mathematical Physics, Spectral Theory, Dynamical Systems, Harmonic Analysis, Partial Differential Equations

Undergrad Research:

I am also interested in working with undergraduate students on projects that are related to my research. If you are currently UML undergraduate students who wish to participate in research projects, feel free to contact with me. Here is an example undergraduate research project on Landscape Theory that I instructed (together with Ilya Kachkovskiy) at Michigan State University in spring 2019.

Education & Employment:

2022-present: Assistant Professor, Department of Mathematical Sciences, UMass Lowell
2019-2022: 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.

Preprints/Publications:

D. N. Arnold, S. Mayboroda, W. Wang and S. Zhang, Numerical analysis on the practical landscape law. In preparation.
I. Chenn, S. Mayboroda, W. Wang, and S. Zhang. On a Novel Effective Equation of the Reduced Hartree-Fock Theory. arXiv:2106.13887. submitted.
I. Chenn, S. Zhang. On the Reduced Hartree-Fock Equation with Anderson Type Background Charge Distribution. arXiv:2105.00295. To appear in Journal of Functional Analysis 2022.
I. Chenn, W. Wang, and S. Zhang, Approximating the Ground State Eigenvalue via the Landscape Potential. Approximating the Ground State Eigenvalue via the Landscape Potential. Nonlinearity 35.6 (2022): 3004.
D. N. Arnold, M. Filoche, S. Mayboroda, W. Wang and S. Zhang, The landscape law for tight binding Hamiltonians. To appear in Commun. Math. Phys. 2022.
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. Physical Review A 104, no. 1 (2021): 012207.
S. Jitomirskaya, S. Zhang, Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators. J. Eur. Math. Soc. (2021).
W. Wang, S. Zhang, The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions, Ann. Henri Poincare, 22, 1429-1457 (2021).
R. Han, F. Yang and S. Zhang, Spectral dimension for β-almost periodic singular Jacobi operators and the extended Harper's model. Journal d'Analyse Mathématique, 142, no. 2 (2020): 605-666.
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.
R. Han, S. Zhang, Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles. Int. Math. Res. Not., rnz319, (2020).
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 (2019).
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, 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.

Seminar Talks:

Colloquium talk, Department of Mathematical Sciences, UMass Lowell, MA, March 4, 2022
(Virtual) Colloquium talk, Department of Mathematics, Wichita State University, KS, January 31, 2022
(Virtual) Colloquium talk, Department of Mathematics, University of Illinois at Chicago, January 13, 2022
(Virtual) Seminar talk on "Functional analysis, operator theory and dynamical systems" to Leipzig and Potsdam, January 12, 2022
(Virtual) Colloquium Talk, Department of mathematics and statistics, University of Reading, UK, October 13, 2021
(Virtual) Colloquium Talk, Department of Mathematics, King's College London, UK, August 4, 2021
Math Physics Seminar Zoom Talk, UCI, CA, April 15, 2021
Math Physics and Operator Algebra Seminar Zoom Talk, MSU, MI, Mar 09, 2021
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:

Simons Collaboration on Localization of Waves Annual Meeting, New York, NY, Feb 17-18, 2022
AMS Special Session Zoom Talk, San Francisco State University, CA, May 1st, 2021
Proposed mini-course speaker for the proposed Summer School on Periodic and Ergodic Spectral Problems, to be held Summer 2022 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:

(Virtual) Colloquium talk, Department of Mathematics, California State University, Los Angeles, CA, January 26, 2022
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

Awards/Honors:

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

Teaching at Umass Lowell:

Math 1290, Calculus 1 B, Fall 2022.

Past Teaching:

Math 5651, Basic Theory of Probability and Statistics, Spring 2022, UMN.
Math 1271, Calculus I, Fall 2021, UMN.
MATH 4512, Differential Equations with Applications, Spring 2021, UMN.
Math 1271, Calculus I, Fall 2020, UMN.
Math 1271, Calculus I, Fall 2019, UMN.
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.
Spring 2019, Math 309. Class Webpage, MSU.
Fall 2018, Math 132. Class Webpage, MSU.
Spring 2018, Math 132. Class Webpage, MSU.
Fall 2017, Math 133. Class Webpage, MSU.
Spring 2017, Math 132. Class Webpage, MSU.
Fall 2016, Math 133. Class Webpage, MSU.
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