Welcome! This page contains all of the basic info about my research interests and my publications. If you have any questions or would like to get in contact with me about physics, feel free to email me at the address below.
Contact info: matthew.lapa.physics@gmail.com
In July 2021 I finished my postdoc at University of Chicago, and I am currently working in industry as a Data/Decision Scientist. However, I still maintain an active interest in physics and do publish new work from time to time. I also have a separate blog on statistics at mattlapa.com that may be of interest to other Data Scientists.
As a graduate student and postdoc I worked on a wide variety of topics in the areas of topological phases of matter, quantum field theory, mathematical physics, and fluid dynamics. As a graduate student I worked mostly on fluid dynamics, symmetry-protected topological (SPT) phases, and geometric aspects of quantum Hall states. I also worked a bit on the arctic curve problem for integrable models in statistical mechanics.
As a postdoc I worked on topological superconductivity beyond the mean-field approximation and several topics in mathematical physics including (i) the stability of gapped phases to long-range interactions, and (ii) the stability of gapless free fermions to interactions and disorder.
In 2019 I gave a talk at the Simons Center for Geometry and Physics on the mathematical structure of the effective hydrodynamics of fractional quantum Hall states. The video of this talk can be found here.
A talk on my recent rigorous work on topological superconductivity with particle number conservation (in collaboration with Michael Levin) can be found here.
Here is a talk on the stability of gapped phases to long-range interactions (also in collaboration with Michael Levin).
Here is a talk on the stability of gapless free fermions to interactions (specifically, on momentum occupation numbers in interacting fermion systems).
Preprints for all of my publications can be found here. Links to preprints and published versions for some selected papers are given below.
University of Chicago (July 2018 - June 2021)
Postdoctoral fellow at the Kadanoff Center for Theoretical Physics.
I was also a Simons Foundation Ultra-Quantum Matter Postdoctoral Fellow from 2019 to 2021, see https://projects.iq.harvard.edu/ultra-qm/postdoctoral-fellows .
University of Illinois at Urbana-Champaign (August 2012 - May 2018)
Ph.D. in Physics. Advisor: Professor Taylor L. Hughes.
Cornell University (August 2008 - May 2012)
B.S. in Engineering Physics, Minor in Applied Mathematics.
MFL and Michael Levin. "Stability of ground state degeneracy to long-range interactions." arXiv:2107.11396.
MFL. "Momentum occupation number bounds for interacting fermions." arXiv:2106.13818.
MFL. "Topology of superconductors beyond mean-field theory." Phys. Rev. Research 2, 033309 (2020). arXiv:2003.05948.
MFL and Michael Levin. "Rigorous results on topological superconductivity with particle number conservation ." Phys. Rev. Lett. 124, 257002 (2020). arXiv:1912.12307.
MFL and Taylor L. Hughes. "Semi-classical wave packet dynamics in non-uniform electric fields ." Phys. Rev. B 99, 121111(R) (2019). arXiv:1812.10497. (Rapid Communication in PRB)
Philippe Di Francesco and MFL. "Arctic curves in path models from the Tangent Method." J. Phys. A: Math. Theor. 51 155202 (2018). arXiv:1711.03182. (Chosen as a highlight paper in J. Phys. A for 2018: https://iopscience.iop.org/journal/1751-8121/page/Highlights-of-2018 ).
MFL and Taylor L. Hughes. "Swimming at low Reynolds number in fluids with odd, or Hall, viscosity." Phys. Rev. E 89, 043019 (2014). arXiv:1310.6270. (Editors' Suggestion in Physical Review E)