# Mathematics and Photonics Research

### current research topics

- Signatures of topological insulators (the Bott index, local signatures in real space).
- Photonics.
- Higher order topological insulators.
- K-theory.
- C*-algebras.
- Uniform joint approximate diagonalization.
- Numerical functional calculus (matrix functions).

### Research links

Slides from my 2021
talk in the Mathematical Physics semiar at Princeton, "Emergent topology from finite volume
topological insulators".
A website promoting the localizer in
operator theory and quantum mechanics.
Supplemental files to
"Surfaces and hypersurfaces as the joint spectrum of matrices" by DeBonis, Loring and Sverdlov.
Slides from my 2019 talk at CMO Oaxaca,
workwhop on Topological Phases of Interacting Quantum Systems,
talk titled "The spectral localizer for estimating bulk gaps and calculating K-theory".
ArXiv feed. Preprints of
my papers are on the Arxiv and they are not always close to the final
version.
*CV with full list of publications.*
My writings and citations listed at Google Scholar.
Real, sparse and skew-symmetric matrices,
a sample.
My dissertation,
The Torus and Noncommutative Topology.
*Et Cetera*.
### Nanostructure Physics department at Sandia National Laboratories

My research with Alex Cerjan,
of the Nanostructure Physics department,
the Center for Integrated Nanotechnologies,
is supported by a subarward from Sandia National Laboratories.