Welters, Aaron
Aaron Welters
Associate Professor  College of Engineering and Science  Mathematics and Systems Engineering
Contact Information
Personal Overview
I am an Associate Professor in the Department of Mathematics and Systems Engineering (MSE) at Florida Tech (FIT). Before coming to FIT, I was held a twoyear postdoctoral position (from 20122014) 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). During 20112012, I was a VIGRE Postdoctoral Researcher in the Department of Mathematics at Louisiana State University (LSU).
Educational Background
Ph.D., Mathematics, University of CaliforniaIrvine, Irvine, CA
B.A., Mathematics, St. Cloud State University, St. Cloud, MN
Selected Publications
Here is a list of my publications and preprints.
 G. W. Milton and A. Welters, Complete characterization of symmetric KuboAndo operator means satisfying Molnar's weak associativity, arXiv:2405.20108 [math.FA] (preprint). doi: 10.48550/arXiv.2405.20108
 A. Stefan and A. Welters, Continuity of the roots of a nonmonic polynomial and applications in multivariate stability theory, arXiv:2112.14287 [math.CA] (preprint). doi: 10.48550/arXiv.2112.14287
 K. Beard and A. Welters, Matrix monotonicity and concavity of the principal pivot transform, Linear Algebra Appl., 628, 323350 (Feb. 1, 2024). doi: 10.1016/j.laa.2023.11.016
 B. Alshammari and A. Welters, On the spectral theory of linear differentialalgebraic equations with periodic coefficients, Journal of Analysis and Mathematical Physics, 13(94) (2023). doi: 10.1007/s13324023008560
 K. Beard, A. Stefan, R. Viator, and A. Welters, Effective operators and their variational principles for discrete electrical network problems, J. Math. Phys., 64(7), 073501 (2023). doi: 10.1063/5.0130429
 A. Stefan and A., Welters, Extension of the Bessmertnyĭ Realization Theorem for Rational Functions of Several Complex Variables. Complex Anal. Oper. Theory 15, 115 (2021). doi: 10.1007/s11785021011502
 A. Stefan and A. Welters, A short proof of the symmetric determinantal representation of polynomials, Linear Algebra Appl., 627, 8093 (2021). doi: 10.1016/j.laa.2021.06.007
 M. Cassier, A. Welters, and G. W. Milton, A rigorous approach to the field recursion method for twocomponent composites with isotropic phases, Chap. 10 in: G. W. Milton (editor), Extending the Theory of Composites to Other Areas of Science. MiltonPatterson Publishing, Salt Lake City, UT, 2016. ISBN: 9781483569192. doi: 10.48550/arXiv.1601.01378
 M. Cassier, A. Welters, and G. W. Milton, Analyticity of the DirichlettoNeumann map for the timeharmonic Maxwell's equations, Chap. 4 in: G. W. Milton (editor), Extending the Theory of Composites to Other Areas of Science. MiltonPatterson Publishing, Salt Lake City, UT, 2016. ISBN: 9781483569192. doi: 10.48550/arXiv.1512.05838
 A. Figotin and A. Welters, On overdamping phenomena in gyroscopic systems composed of highloss and lossless components, J. Math. Phys. 57, 042902 (2016) doi: 10.1063/1.4944721

S. P. Shipman and A. Welters, Pathological scattering by a defect in a slowlight periodic layered medium, J. Math. Phys. 57, 022902 (2016). doi: 10.1063/1.4941137
 A. Figotin and A. Welters, Lagrangian framework for systems composed of highloss and lossless components, J. Math. Phys. 55, 062902 (2014). doi: 10.1063/1.4884298
 A. Welters, Y. Avniel, and S. G. Johnson, Speedoflight limitations in passive linear media, Phys. Rev. A 90, 023847 (2014). doi: 10.1103/PhysRevA.90.023847
 S. P. Shipman and A. Welters, Resonant electromagnetic scattering in anisotropic layered media, J. Math. Phys. 54, 103511 (2013). doi: 10.1063/1.4824686
 S. P. Shipman and A. Welters, Resonance in anisotropic layered media, 2012 International Conference on Mathematical Methods in Electromagnetic Theory, 2012, pp. 227232, doi: 10.1109/MMET.2012.6331235
 A. Figotin and A. Welters, Dissipative properties of systems composed of highloss and lossless components, J. Math. Phys. 53, 123508 (2012). doi: 10.1063/1.4761819
 A. Welters, On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block, SIAM J. Matrix Anal. Appl., 32:1, 122 (2011). doi: 10.1137/090761215
 A. Welters, On the Mathematics of Slow Light. Thesis (Ph.D.)Univ. of Calif., Irvine. ProQuest LLC, Ann Arbor, MI, 2011.
Recognition & Awards
Aaron Welters (PI) and Xianqi Li (CoPI), Collaborative Research: Datadriven Realization of Statespace Dynamical Systems via Lowcomplexity Algorithms, National Science Foundation (NSF), $125,000, Aug. 1, 2024July 31, 2027, Grant no.: DMS 2410678.
Aaron Welters (PI), Variational principles, bounds, and realizability of effective operators for metamaterial synthesis using multphase composites, Simons Foundation, Travel Support for Mathematicians, $42,000 ($8,400/year), Sept. 1, 2023Aug. 31, 2028, Gift ID: MPSTSM00002799.
Aaron Welters (PI), YIP early career award, On a Theory of Broadband Absorption Suppression in Magnetic Composites, Air Force Office of Science Research (AFOSR), $264,199.41, Apr. 1, 2015Mar. 31, 2018, AFOSR Grant no.: FA95501510086. AFOSR Program Officer: Dr. Arje Nachman, Electromagnetics. Technical report @ https://apps.dtic.mil/sti/pdfs/AD1058297.pdf
Research
Research Interests:
 Applied mathematics
 Mathematical physics
Focus Areas:
 Electromagnetics
 Material science (composites and effective media)
 Dissipative systems
Mathematical Specializations:
 Linear algebra
 Functional analysis
 Spectral and scattering theory
 Perturbation theory
 Passive linear systems theory
 HerglotzNevanlinna functions
Current/Past Research Topics:
 Positive operator means (e.g., KuboAndo means)
 Monotonicity and concavity/convexity properties of matrix functions
 Spectral theory of linear differentialalgebraic equations (DAEs)
 Realizability theory of multivariate functions (e.g., Bessmertnyi realizations, effective operator representations)
 Theory of composites and its extensions
 HerglotzNevanlinna functions and their applications
 Broadband absorption suppression in magnetic composites
 Slowlight enhancement of lightmatter interactions
 Speedoflight 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]
Current/Past Ph.D students:
 Anthony Stefan  Expected Graduation Date: May 2025
 Dissertation title (tentative): Bessmertny ̆ı realizations of effective tensors with symmetries in multiphase composites for metamaterial synthesis.
 Bader Alshammari  Graduation Date: July 2022
 Dissertation title: On the Spectral Theory of Linear DifferentialAlgebraic Operators with Periodic Coefficients
 http://hdl.handle.net/11141/3571
Current/Past MS students (with Thesis):
 Kenneth Beard  Graduation Date: May 2022
 Thesis title: Relaxation of Variational Principles for Zproblems in Effective Media Theory
 http://hdl.handle.net/11141/3497
 Anthony Stefan  Graduation Date: May 2021
 Thesis title: Schur Complement Algebra and Operations with Applications in Multivariate Functions, Realizations, and Representations
 http://hdl.handle.net/11141/3260