Mathematics Research

Interests and Background

In general I have a very broad interest in plasma physics, geometric control theory, PDE, applied mathematics, geometric analysis, and contact geometry. However, my attention is currently focused on the use of Exterior Differential Systems (EDS), Cartan's method of Equivalence, and moving frames to study problems in plasma physics with applications to Stellarator fusion devices. My other main research area is geometric control theory via Cartan type methods. I have also been working on a project related to bi-contact geometry and would like to expand my research further in this direction. My full length thesis ) is in the area of geometric control theory, specifically relating to the theory of cascade feedback linearization of control systems with symmetry, which in turn has important implications for the study of dynamic feedback linearizable control systems. My thesis draws on subjects such as EDS, Goursat bundles, Calculus of Variations, and Lie algebras. It's a very enjoyable overlap of subjects and I hope to continue finding more tools from other areas in geometry to answer questions in control theory. My advisor was the excellent Professor Jeanne Clelland with Peter Vassiliou as my wonderful co-advisor.

My advisor and I authored this paper in the Archive for Rational Mechanics. It gives further explicit results on the ``rarity" of Beltrami fields with non-constant proportionality factor. These types of solutions are of interest to the areas of hydrodynamics and plasma physics.

Here is my C.V.


Published and Accepted Work


  1. T.J. Klotz, P. Vassiliou. Quotients of Invariant Control Systems, accepted pending revisions.
  2. J. Clelland, T. Klotz, P. Vassiliou. Dynamic Feedback Linearization of Control Systems with Symmetry, 2024. SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 20, 058 (Special Issue on Symmetry, Invariants, and their Applications in honor of Peter J. Olver)
  3. R. Carney, M. Chyba, and T. Klotz, 2024. Using hybrid automata to model mitigation of global disease spread via travel restriction, Networks \& Heterogeneous Media 19 (1)
  4. Klotz, T.J., 2023. Geometry of cascade feedback linearizable control systems. Differential Geometry and its Applications, 90, p.102044.
  5. Chyba, M., Klotz, T., Mileyko, Y. and Shanbrom, C., 2023. A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation. Mathematics of Control, Signals, and Systems, pp.1-31.
  6. Burby, J. W., and T. J. Klotz. ``Slow manifold reduction for plasma science." Communications in Nonlinear Science and Numerical Simulation (2020): 105289.
  7. Clelland, Jeanne N., and Taylor Klotz. "Beltrami fields with nonconstant proportionality factor." Archive for Rational Mechanics and Analysis 236.2 (2020): 767-800.
  8. G. Dean, T. Klotz, B. Prinari and F. Vitale, ``Dark-Dark and Dark-Bright Soliton Interactions in the two-component Defocusing Nonlinear Schrodinger Equation'', Applic. Anal., Vol.92, pp. 379-397 (2013)

In Progress and Submitted

  1. T. Klotz and P. Vassiliou. Orbital Feedback Linearization: Geometric Characterization & Construction
  2. T. Klotz and G. Wilkens. Some Local Geometry of Bi-Contact Structures, current arxiv version
  3. Some Geometry of Magnetic Fields for Plasma Confinement in the Style of Cartan, in preparation
  4. Pseudo-Focal Surfaces, in preparation
  5. Local Geometry of Bi-Contact Structures: Applications, in preparation



Before my current work, my first two years of graduate school were spent studying fluid equations from the perspective of infinite-dimensional Riemannian geometry. For example, the Euler equations for incompressible fluid flow on a finite dimensional manifold are precisely the Euler-Arnold equations on the space of volume preserving diffeomorphisms (endowed with an appropriate metric, that is). I still find this area interesting! Perhaps if the Universe allows I will return to these topics someday in a more serious way.