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Links:
Math Department
LSU Home Page
Am. Math Soc.
Math. Assoc. Am.
Nat. Sci. Found.
Siblinks:
Barbara
Michael
Patrick
Art
Birds
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Welcome to my mathematics website.
My research concerns the mathematics that arises in the study of waves in composite
media.
The problems I investigate concern the following topics.
- Spectral theory of differential and integral operators
- Electromagnetic resonance; meta-materials
- Coupled nonlinear dispersive systems; polariton equations
Link to PUBLICATIONS. Here are some recent works on the Fermi surface:
- [FLS21]
Reducible Fermi surface for multi-layer quantum graphs including stacked graphene,
Lee Fisher and Wei Li and Stephen P. Shipman,
Comm. Math. Phys., in press (2021).
arXiv
- [LS20]
Irreducibility of the Fermi Surface for Planar Periodic Graph Operators,
Wei Li and Stephen P. Shipman, Lett. Math. Phys. 110 (2020) 2543-2572.
arXiv
- [S19]
Reducible Fermi Surfaces for Non-symmetric Bilayer Quantum-Graph Operators,
Stephen P. Shipman, J. Spectral Theory (2019) online 2019/09/16.
arXiv
- [S14]
Eigenfunctions of Unbounded Support for Embedded Eigenvalues of Locally Perturbed Periodic Graph Operators,
Stephen P. Shipman,
Comm. Math. Phys., Vol. 332(2) (2014) 605-626.
arXiv
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Research group at LSU
- Stephen Shipman
- Daniel Massatt (Asst Prof Math)
- Justin Wilson (Asst Prof Physics)
- Ilya Vekhter (Prof Physics)
- Doosung Choi (Postdoc)
- Alina Oktyabrskaya (doctoral student)
- Haley Jay Garcia (undergraduate)
- David Aiken (undergraduate)
- Carmen Neill (undergraduate)
- Amelia Fargason (undergraduate)
Postdoctoral associates
- Doosung Choi, Fall 2022-
- Wei Li, Spring 2018-Summer 2020 (Presently Asst. Prof. at DePaul University)
- Cristi Guevara, Fall 2014-Fall 2017 (Presently at Decision Center for Educational Excellence at AZ State)
- Aaron Welters, Fall 2011-Spring 2012 (Presently Ass. Prof. at FIT)
Past Ph.D. advisees
- Jorge Villalobos, Ph.D. 2024
- Lee Fisher, Ph.D. 2023
- Zhaoxia "Mary" Wang, Ph.D. 2018
- Emily McHenry, Ph.D. 2017
- Gayan Abeynanda, Ph.D. 2016
- Hairui Tu, Ph.D. 2011
- Santiago Fortes, Ph.D. 2010
- Natalia Ptitsyna, Ph.D. 2009
Funding
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My research has been funded by five grants from the National Science Foundation and by the LSU Board of Regents. See the "Funding" link in the sidebar.
Associate editor
- SIAM J Appl Math (SIAP)
- Results in Appl Math (RINAM)
- Analysis and Math Phys (AAMP)
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UH-TAMU-LSU Undergraduate Math Conference
This semi-local annual conference is a sharing of the undergraduate research programs at UH, TX A&M and LSU. Here are links to the past conferences:
2024
2023
2022
2020
2019
2018
2017
NSF-supported GUI for EM in layered media
(online graphical user interface coming "soon")
- Recent contributors:
- Aaron Welters (FIT)
- Andrew Welters
- Joel Keller (math major)
Research experiences for undergraduates
By carefully selecting projects, mentoring undergraduates can be rewarding for student and mentor. Read about the projects of my students at the REU link. Some of them are
- Toy Model for Density of Bound States
- Misconceptions in Vector Calculus
- Structure vs. Spectra for Quantum Graphs
- Modes and Resonance in Anisotropic Media
- Lattice Model for Metamaterials
Math Consultation Clinic
In the MCC, graduate students manage teams of undergraduate students in problems from other disciplines and research entities and companies on and off the LSU campus.
Opportunities for undergraduate students
This link lists opportunities for undergraduate mathematics majors to become involved in research. We encourage our majors to begin early. Students may contact me about this. Take a look at some of the current PROJECTS in mathematics that involve undergraduates.
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My mathematics studies transpired at the University of Arizona in Tucson.
Under the direction of Prof.
Nicholas Ercolani an increasing number of years ago, I completed my Ph.D. on the topic "A continuum limit of a finite discrete nonlinear Schrödinger system."
This is my trajectory anti-chronologically:
Professor, Louisiana State University (2014-)
Visitor, Institute for Mathematics and its Applications, Minneapolis, MN (Fall 2016)
Associate Professor, Louisiana State University (2008-2014)
Visiting Researcher, Universidad Carlos III, Madrid (Fall 2010)
Research Scientist, Courant Institute, NYU (2006-'07)
Visiting Professor, Institut Élie Cartan, Nancy, France (summer, 2006)
Assistant Professor, Louisiana State University (2002-'08)
Visiting Assistant Professor, Duke University (2001-'02)
Assistant Research Professor, Duke University (-2001)
Ph.D, University of Arizona,
advisor:
Nicholas Ercolani
Some awards:
2019 LSU College of Science Graduate Teaching Award
2015 LSU Alumni Association Faculty Excellence Award
2015 LSU Tiger Foundation Undergraduate Teaching Award
2014 Dr. Marion "Soc" Socolofsky Award for Teaching Excellence, LSU College of Science
2012 N. A. Khizhnyak Award, by the International Conference on Mathematical Methods in Electromagnetic Theory in Ukraine, "for the Contribution to Electromagnetic Theory"
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