Mathematics and Photonics Research
current research topics
 Signatures of topological insulators (the Bott index, local signatures in real space).
 Photonics.
 Higher order topological insulators.
 Ktheory.
 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 Ktheory".
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 skewsymmetric matrices,
a sample.
My dissertation,
The Torus and Noncommutative Topology.
Et Cetera.
Articles submitted or published recently

Terry A. Loring, Jianfeng Lu, Alexander B. Watson.
Locality of the windowed local density of states.

Terry Loring, Fredy Vides.
Computing Floquet Hamiltonians with Symmetries.
Journal of Mathematical Physics, 61(11): 113501, 2020.

Jonathan Michala, Alexander Pierson, Terry A. Loring, Alexander B. Watson.
Wavepacket propagation in a
finite topological insulator and the spectral localizer index.
Involve, a Journal of Mathematics 14:2 (2021): 209239.

Patrick H. DeBonis, Terry A. Loring, Roman Sverdlov.
Surfaces and hypersurfaces as the joint spectrum of matrices.
Arxiv:1911.00751. Rocky Mountain Math Journal, to appear.

Alexander Cerjan, Terry A. Loring.
Local invariants identify topological metals.
Arxiv:2112.08623.

Alexander Cerjan, Fredy Vides, Terry A. Loring.
Quadratic pseudospectrum for identifying localized states.
Arxiv:2204.10450.
National Science Foundation
I have support from the National Science Foundation, DMS2110398,
"Numerical Methods in Noncommutative Matrix Analysis."
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.