Picture Profile

Welcome to my mathematics homepage. Interested in my research? Look at my research statement (before 2015).

I am an Assistant Professor of Mathematical Sciences in the Department of Mathematical Sciences at Florida Institute of Technology (FIT). I was just awarded a 3-year AFOSR YIP grant through the Air Force's Young Investigator Research Program (YIP) on my research proposal entitled, "On a Theory of Broadband Absorption Suppression in Magnetic Composites." The news story announcing the AFOSR YIP award winners can be found on the AFOSR website here or on EurekAlert (AAAS Science News website) here.

I recently completed a two-year (2012-2014) 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 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. From 2012-2014 I was at MIT where, in addition to teaching, I worked with my co-authors 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 and theory of Herglotz functions). 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, teaching and beginning my 2nd year as a faculty member at FIT.

Contact Info:

Dr. Aaron Welters
Assistant Professor of Mathematical Sciences
Department of Mathematical Sciences
Florida Institute of Technology
Melbourne, FL 32901
(321) 674-7202 (Office)
awelters [at] fit dot edu