Mathematics Research

Interests and Background

Generally, my research focuses on the geometry of differential equations and their applications; from PDEs in plasma physics, to engineering control systems and biology, and even dynamical systems and chaos. 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 style 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.


Here is my C.V.


Published and Accepted Work


  1. T.J. Klotz, P. Vassiliou. Quotients of Invariant Control Systems, 2025 AIMS on Applied Mathematics: GEOMETRY, TOPOLOGY AND CONTROL SYSTEM DESIGN: Proceedings of a Banff International Research Station Workshop. < a href="https://arxiv.org/abs/2508.01038" style="color:cyan">current arxiv version
  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)

Under Review

  1. J.W. Burby, N. Duignan, T.J. Klotz, J.D. Meiss. All field strengths are possible locally in Boozer coordinates current arxiv version
  2. T. Klotz and P. Vassiliou. Flatness of the Generic Under-Actuated 6-Degrees-of-Freedom Unmanned Surface Vessel, current arxiv version
  3. T. Klotz and P. Vassiliou. Orbital Feedback Linearization: Geometric Characterization & Construction
  4. T. Klotz and G. Wilkens. Some Local Geometry of Bi-Contact Structures, current arxiv version



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.