I am an Assistant Professor of Mathematical Sciences in the Department of Mathematical Sciences at Florida Institute of Technology (FIT). I recently completed a two-year postdoctoral position as an Applied Mathematics Instructor in the Department of Mathematics at Massachusetts Institute of Technology (MIT). In 2011, I completed my Ph.D. in Mathematics at the University of California, Irvine (UCI). At UCI, I was part of the Math Physics Group which includes my Ph.D. advisor (and collaborator) Alex Figotin. During 2011-2012, I was a VIGRE Postdoctoral Researcher in the Department of Mathematics at Louisiana State University (LSU). At LSU, I was part of the Mathematics of Material Science research group working closely with my collaborator Stephen Shipman. During the summer of 2012, I was an Assistant Project Scientist at UCI working with Alex Figotin. From 2012-2014, I was at MIT where, in addition to teaching, I worked with my collaborators Steven G. Johnson and Yehuda Avniel.
B.A., Mathematics, St. Cloud State University, St. Cloud, MN
Ph.D., Mathematics, University of California-Irvine, Irvine, CA
I am currently teaching and modifying the graduate course MTH5201-Mathematical Methods in Science and Engineering 1. The course topics include the following: Fourier series and their convergence properties; Sturm-Liouville eigenfunction expansion theory; Bessel and Legendre functions; solution of heat, wave and Laplace equations by separation of variables in Cartesian coordinates.
Here is a list of my publications and works in progress.
- S. P. Shipman and A. Welters, Pathological scattering by a defect in a slow-light medium. Submitted.
- A. Figotin and A. Welters, Lagrangian framework for systems composed of high-loss and lossless components, J. Math. Phys., vol. 55, no. 6, eid: 062902, pp. 1-39, 2014.
- A. Welters, Y. Avniel, and S. G. Johnson, Speed-of-light limitations in passive linear media, Phys. Rev. A, vol. 90, no. 2, pp. 023847:1-17, 2014.
- S. P. Shipman and A. Welters, Resonant electromagnetic scattering in anisotropic layered media, J. Math. Phys., vol. 54, no. 10, eid: 103511, pp. 1-40, 2013.
- S. P. Shipman and A. Welters, Resonance in anisotropic layered media, Proceedings of the 14th International Conference on Mathematical Methods in Electrodynamic Theory (MMET12 Kharkov), pp. 227-232, 2012.
- A. Figotin and A. Welters, Dissipative properties of systems composed of high-loss and lossless components, J. Math. Phys., vol. 53, no. 12, eid: 123508, pp. 1-40, 2012.
- A. Welters, On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block, SIAM J. Matrix Anal. Appl., vol. 32, no. 1, pp. 1-22, 2011.
- A. Welters, On the Mathematics of Slow Light. Thesis (Ph.D.)-Univ. of Calif., Irvine. ProQuest LLC, Ann Arbor, MI, 2011.
- Mathematical physics & Applied mathematics
- Material science
- Dissipative systems
- Functional analysis
- Spectral and scattering theory
- Perturbation theory
- Linear response theory
Current Project Interests:
- Broadband absorption suppression in magnetic composites
- Slow-light enhancement of light-matter interactions
- Speed-of-light limitations in complex media
- Wave propagation in complex and periodic media [e.g., metamaterials, composites, photonic crystals, materials with defects, slow and fast light, guided modes (i.e., embedded eigenvalues), resonance phenomena]