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Welcome to my mathematics homepage. Interested in my research? Look at my research statement.

I am currently an Applied Mathematics Instructor in the Department of Mathematics at Massachusetts Institute of Technology (MIT), but have recently accepted a faculty appointment (starting Aug. 11, 2014) as Assistant Professor of Mathematical Sciences in the Department of Mathematical Sciences at Florida Institute of Technology (FIT). I completed my Ph.D. in Mathematics at the University of California, Irvine (UCI) in 2011. At UCI, I was part of the Math Physics Group which includes my Ph.D. advisor (and co-author) 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 co-author Stephen Shipman. During the summer of 2012, I was an Assistant Project Scientist at UCI working with Alex Figotin. I have been at MIT since Sept. 2012 where, in addition to teaching, I work with my collaborators Steven Johnson and Yehuda Avniel.

RESEARCH INTERESTS

My research interests are in mathematical physics and applied mathematics. I focus on the areas of electromagnetics, material science, and dissipative systems. My mathematical specializations are in functional analysis, spectral and scattering theory, perturbation theory (with a focus on non-self-adjoint linear operators and nonlinear eigenvalue problems), and linear response theory (with a focus on passive linear systems). I apply the mathematical methods from these areas to study problems involving 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].

News

I am currently doing research, writing papers, applying for grants, and preparing to begin my faculty position at FIT.

Contact Info:

Dr. Aaron Welters
Applied Mathematics Instructor
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139-4307
(617) 253-6770 (Office)
awelters [at] math mit edu