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

Here is my CV.

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.

- 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.

- 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.

- 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).