#
Jacob Shapiro's Homepage at the Math Department of Columbia University

## About

I am a postdoctoral fellow sponsored by Prof. M. I. Weinstein. I did my PhD in mathematical physics with Prof. G. M. Graf and graduated in September 2018.
### Contact

Please e-mail me at shapiro@math.columbia.edu.
## Research

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

### Articles

orcid.org/0000-0003-0732-393X
- with Fonseca, Sheta, Wang, Yamakawa: Two-dimensional time-reversal-invariant topological insulators via Fredholm theory (2019); arXiv.
- The topology of mobility-gapped insulators (2018); arXiv.
- with Tauber, C.: Strongly disordered Floquet topological systems (2018); Annales Henri PoincarĂ© (2019) 20(6), 1837-1875; arXiv.
- with Graf, G.M.: Complete localization for disordered chiral chains (pre-print to appear soon, see corresponding chapter in PhD thesis below).
- with Graf, G.M.: The bulk-edge correspondence for disordered chiral chains. Commun. Math. Phys. (2018) 363: 829.; arXiv.
- The bulk-edge correspondence in three simple cases (2017); Rev. Math. Phys.; arXiv.

### Manuscripts

## Teaching