Mathematics and Related Research
current research topics
- Signatures of topological insulators (the Bott index, local signatures in real space).
- Uniform joint approximate diagonalization.
- Numerical functional calculus (matrix functions).
Slides from my 2020
talk at the annual AMS meeting, "A numerical approach to Chern numbers
and unbounded Fredholm modules". I had issues embedding the videos, so
these are separate files:
edge mode around defect,
edge mode around clean system,
edge mode for square with disorder,
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
CV with full list of publications.
user page Math Overflow.
My writings and citations listed at Google Scholar.
My ORC ID and another listing of some of my writings.
The Torus and Noncommutative Topology.
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.
Wave-packet propagation in a finite topological insulator and the spectral localizer index.
Patrick H. DeBonis, Terry A. Loring, Roman Sverdlov.
Surfaces and hypersurfaces as the joint spectrum of matrices.
Terry A. Loring.
A Guide to the Bott Index and Localizer Index
Terry A. Loring.
Bulk Spectrum and K-theory for Infinite-Area Topological Quascrystal
Journal of Mathematical Physics,60(8):081903 (2019).
- My research has been supported, in part, for many years by the
Efroymson Foundation. My research on generator and relations in
C*-algebras is looking more and more like real algebraic geometry,
albeit in a noncommutative setting. I trust that
- I also have support from the National Science Foundation, DMS1700102,
"Emergent Topology and K-Theory of Matrix Models."