Shiwen Zhang

Assistant Professor

Department of Mathematics & Statistics
University of Massachusetts Lowell
Southwick Hall
11 University Ave.
Lowell, MA 01854

Office: Southwick Hall 350K
Email: shiwen_zhang@uml.edu

I am an Assistant Professor at the Department of Mathematics & Statistics 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

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.

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:

L. Shou, W. Wang, S. Zhang, Landscape estimates of the integrated density of states for Jacobi operators on graphs. arXiv:2406.06794. submitted.
L. Shou, W. Wang, S. Zhang, Landscape approximation of the ground state eigenvalue for graphs and random hopping models. Journal of Functional Analysis 286.7 (2024): 110339.
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, S. Zhang. On an Effective Equation of the Reduced Hartree-Fock Theory. Advanced Nonlinear Studies 23.1 (2023): 20220070.
I. Chenn, S. Zhang, On the reduced Hartree-Fock equations with a Small Anderson Type Background Charge Distribution. Journal of Functional Analysis (2022): 109702.
I. Chenn, W. Wang, and S. Zhang, Approximating the Ground State Eigenvalue via the Landscape Potential. Nonlinearity 35.6 (2022): 3004.
D. N. Arnold, M. Filoche, S. Mayboroda, W. Wang, S. Zhang, The landscape law for tight binding Hamiltonians. Communications in Mathematical Physics (2022): 1-53.
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).
Lecture Notes. S. Jitomirskaya, W. Liu and S. Zhang, Arithmetic spectral transitions: a competition between hyperbolicity and the arithmetics of small denominators. in Harmonic analysis and applications. Vol. 27. American Mathematical Soc., 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, (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

Grants, Funding, and Awards:

National Science Foundation Grant (LEAPS-MPS). DMS-2418611. 2024-2026
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

Conferences/Workshops Organized:

(together with L. Shou): AMS-Spring Eastern Sectional Meeting-Spectral theory and quantum systems. Howard University, Washington, DC 04/6-7/2024
(together with I. Kachkovskiy and M. Cha): AMS-Sectional Meeting-Ergodic and Topological Quantum Systems, Ann Arbor, MI 10/20-21/2018

Recent Seminars, Conferences and Workshops:

Analysis Seminar, Mathematics Department, Rice University 03/05/2024
Applied Math Seminar Talk, UMass Amherst 05/16/2023
Math Physics and Operator Algebras seminar Talk, Michigan State University 04/18/2023
Applied Mathematics Seminar Talk(virtual), Texas Tech University 04/05/2023
Colloquium talk, Department of Mathematical Sciences, UMass Lowell, MA, March 4, 2022
Colloquium talk, Department of Mathematics, Wichita State University, KS, January 31, 2022
Colloquium talk, Department of Mathematics, University of Illinois at Chicago, January 13, 2022
Seminar talk on "Functional analysis, operator theory and dynamical systems" to Leipzig and Potsdam, January 12, 2022
Colloquium Talk, Department of mathematics and statistics, University of Reading, UK, October 13, 2021
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.

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:

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

Student Mentoring and Teaching

2024-2025. Current student. Ipsita Sinha (Master student in Physics, jointly mentor with Hugo Ribeiro).
Fall 2024. Undergrad Senior project. Gregory Yodsnukis.
Spring 2024. Undergrad Senior project. Patrick OKeefe.

UMass Lowell
- Fall 2024. Math4450/5450 Partial differential equations; Math1320 Calculus II.
- Spring 2024. Math1420 Honors Calculus II.
- Fall 2023. Math4450/5450 Partial differential equations.
- Spring 2023. Math1420 Honors Calculus II; Math 1320 Calculus II
- Fall 2022. Calculus 1B.

Past Teaching:

UMN
- Spring 2022. Math 5651 Basic Theory of Probability and Statistics.
- Fall 2021. Math 1271 Calculus I.
- Spring 2021. MATH 4512 Differential Equations with Applications.
- Fall 2020. Math 1271 Calculus I.
- Fall 2019. Math 1271 Calculus I.
MSU
- Fall 2018-Spring 2019. Undergrad Rsearch Program(Discovering America Program) on Landscape theory.
- Summer 2018. TA. Lectures by Svetlana Jitomirskaya at the PCMI Graduate Summer School on Harmonic Analysis, Park City.
- Spring 2019. Math 309 Linear Algebra.
- Fall 2017. Math 133 Calculus II.
- Spring 2017. Math 132 Calculus I.
- Fall 2016. Math 133 Calculus II.
UCI
- Winter 2016. TA. Math 3D Elementary Differential Equation.
- Fall 2015. Instructor. Math 2B Calculus II.
- Summer 2015. TA. Math 176/Econ135: Math of Finance.
- Fall 2014. TA. Math 2B: Calculus II.