About

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Assistant Professor of Mathematical Sciences

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.

  • Phone: (321) 674-7202
  • City: Melbourne, USA
  • Degree: Ph.D. Mathematics
  • Email: awelters@fit.edu

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].

Citations

Publications

Awards/Grants

Graduate Students

Publications

M. Cassier, A. Welters, and G. W. Milton, “Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell’s equations,” in Extending the Theory of Composites to Other Areas of Science (G. W. Milton, ed.), Chap. 4, Milton-Patton Publishing, 2016.ISBN: 978-1-4835-6919-2.

M. Cassier, A. Welters, and G. W. Milton, “A rigorous approach to the field recursion method for two-component composites with isotropic phases,” in Extending the Theory of Composites to Other Areas of Science (G. W. Milton, ed.), Chap. 10, Milton-Patton Publishing, 2016. ISBN: 978-1-4835-6919-2.

A. Figotin and A. Welters, On overdamping phenomena in gyroscopic systems composed of high-loss and lossless components, J. Math. Phys. 57, 042902 (2016).

S. P. Shipman and A. Welters, Pathological scattering by a defect in a slow-light medium, J. Math. Phys., vol. 57, no. 2, eid: 022902, pp. 1–44, 2016.

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.

A. Figotin and A. Welters, Lagrangian framework for systems composed of high-lossand lossless components, J. Math. Phys., vol. 55, no. 6, eid: 062902, pp. 1–39, 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-lossand 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 ofa 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.

CV

Check My CV

Teaching

If you would like to know about my philosophy on teaching you may read my teaching statement. As regards to my experience, I am currently teaching at Florida Institute of Technology (FIT) as an Assistant Professor of Mathematical Sciences (Aug. 2014 - ). I recently taught at the Massachusetts Institute of Technology (MIT) as an Applied Mathematics Instructor (Sept. 2012 - May. 2014). Before this, I taught at Louisiana State University (LSU) from Sept. 2011-May 2012 as a VIGRE Postdoctoral Researcher and I was a teaching assistant at the University of California, Irvine (UCI) from Sept. 2004-Aug. 2006. Below is a list that summarizes this experience.

Assistant Professor at FIT

  • MTH 5102: Linear Algebra
  • MTH 3102: Intro to Linear Algebra
  • MTH 5130: Theory of Complex Variables
  • MTH 1001: Calculus

Applied Mathematics Instructor at MIT

  • MATH 18.02: Calculus (Recitation)
  • MATH 18.100C: Real Analysis
  • MATH 18.03: Differential Equations (Recitation)
  • MATH 18.02A: Calculus (Recitation)
  • MATH 18.01A: Calculus (Recitation)

VIGRE Postdoctoral Researcher at LSU

  • MATH 3355-1: Probability
  • MATH 4997-1 VIR: Electromagnetic Waves in Heterogeneous Structures

Teaching Assistant at UCI

  • MATH 2D: Multivariable Calculus
  • MATH 146: Fourier Analysis
  • MATH 184: History of Mathematics
  • MATH 2B: Single Variable Calculus
  • MATH 2A: Single Variable Calculus
  • MATH 2J: Infinite Series and Linear Algebra

Research Group

My Research Group

Kenneth Lathrom

Master's Student

Anthony Stefan

Doctoral Student

Robert Viator

Visiting Assistant Professor

Contact

Contact Me

My Office

Frederick C. Crawford Bldg, 319

Academic Profiles

Email Me

awelters@fit.edu

Call Me

(321) 674-7202