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Jacob Shapiro's Homepage at the Physics Department of Princeton University

About

I am currently a Lecturer at the physics department working in the mathematical physics group of Prof. M. Aizenman. From January 2020 until August 2021 I was an SNSF postdoctoral fellow in that same group. From October 2018 until December 2019 I was a postdoctoral fellow with Prof. M. I. Weinstein. I did my PhD in mathematical physics with Prof. G. M. Graf and graduated in September 2018.

From July 2022 I will be an assistant professor at the Princeton University math department.

Here is my CV.

Contact

Please e-mail me at jacobshapiro@princeton.edu.

Research

My main research interest is mathematical physics. Specifically, I work on problems from condensed matter physics and statistical mechanics using probability, functional analysis and algebraic topology.

Articles

orcid.org/0000-0003-0732-393X

Dynamical Localization for Random Band Matrices up to W \ll N^{1/4}
Giorgio Cipolloni, Ron Peled, Jeffrey Schenker, Jacob Shapiro
arXiv:2206.05545.
Depinning in the integer-valued Gaussian field and the BKT phase of the 2D Villain model
Michael Aizenman, Matan Harel, Ron Peled, Jacob Shapiro
arXiv:2110.09498v2.
Fredholm homotopies for strongly-disordered 2D insulators
Alex Bols, Jeffrey Schenker, Jacob Shapiro
arXiv:2110.07068.
Incomplete localization for disordered chiral strips
Jacob Shapiro
arXiv:2108.10978.
Is the continuum SSH model topological?
Jacob Shapiro and Michael I. Weinstein
arXiv:2107.09146.
Tight-binding reduction and topological equivalence in strong magnetic fields
Jacob Shapiro and Michael I. Weinstein
Advances in Mathematics Volume 403, 16 July 2022, 108343; arXiv:2010.12097.
Lower bound on quantum tunneling for strong magnetic fields
Charles L. Fefferman, Jacob Shapiro and Michael I. Weinstein
SIAM Journal on Mathematical Analysis 54 (1), 1105-1130; arXiv:2006.08025.
Two-dimensional time-reversal-invariant topological insulators via Fredholm theory
Eli Fonseca, Jacob Shapiro, Ahmed Sheta, Angela Wang and Kohtaro Yamakawa
Mathematical Physics, Analysis and Geometry (2020) 23(29); arXiv:1908.00910.
The topology of mobility-gapped insulators
Jacob Shapiro
Letters in Mathematical Physics (2020); arXiv:1811.07997.
Strongly disordered Floquet topological systems
Jacob Shapiro and Clement Tauber
Annales Henri Poincaré (2019) 20(6), 1837-1875; arXiv:1807.033251.
The bulk-edge correspondence for disordered chiral chains
Gian Michele Graf and Jacob Shapiro
Commun. Math. Phys. (2018) 363: 829.; arXiv:1801.09487.
The bulk-edge correspondence in three simple cases
Jacob Shapiro
Rev. Math. Phys.; arXiv:1710.10649.

Manuscripts

Paris lectures on topological insulators - July 2022
My PhD thesis Topology and Localization: Mathematical Aspects of Electrons in Strongly-Disordered Media.
Notes on "Topological Aspects in Condensed Matter Physics" following a course taught by Prof. G. M. Graf in the Fall semester of 2015.
My MSc thesis The Bulk-Edge Correspondence in Quantum Hall and Topological Insulator Systems.

Presentations

Talk at the One World IAMP Mathematical Physics Seminar in April 2022: Continuum and strongly disordered topological insulators.
Talk at the One World Probability Seminar in February 2022: Delocalization in the integer-valued Gaussian Field and the Berezinskii-Kosterlitz-Thouless phase of the 2D Villain model (the first part of this talk was given by Michael Aizenman).
Talk at the Online North East PDE Seminar (ONEPAS) in March 2021: Tight-binding limits in strong magnetic fields and the integer quantum Hall effect (video).
Talk at IPAM (UCLA) in January 2020 during the Theory and Computation for 2D Materials conference: Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory (video).

Teaching

Material for courses taught.