## Dr. Joel Rosenfeld - Research Mathematician and Engineer

**I am an Assistant Professor in the Department of Mathematics and Statistics at the University of South Florida.** I received my Ph.D. from the Mathematics department at the University of Florida in 2013 under the advisement of Dr. Michael T. Jury studying Operator Theory and Functional Analysis. My work is decidedly interdisciplinary; from 2013 to 2018 I worked as a postdoctoral researcher in engineering departments. I was a postdoc in Mechanical Engineering at the University of Florida under Dr. Warren E. Dixon studying numerical methods in optimal control theory and fractional calculus. Subsequently, I joined the Department of Electrical Engineering and Computer Science at Vanderbilt University under Dr. Taylor T. Johnson studying numerical methods in formal methods for computing, which ultimately led to a position as a Senior Research Scientist Engineer in that same department.

**My research spans the study of RKHSs** from a range of perspectives. This includes the study of RKHSs as they pertain to complex function theory. I have introduced several function spaces to resolve problems in operator theory and numerical analysis. Specifically, I introduced the polylogarithmic Hardy space to give an example of a RKHS that has only trivial densely defined multiplication operators, and I developed the Mittag-Leffler RKHS as a fractional order analogue to the Bargmann-Fock space.

**My applied/engineering research focus is on data driven methods** for the verification and stability of nonlinear and hybrid cyber physical systems. In particular, my work develops innovative machine learning approaches to establishing the stability of approximate online optimal controllers, reachable set over-approximations, and other system invariants by focussing on the development of custom basis functions that reduce the dimensionality of learning problems. For example, this work has led to dramatic improvements in online optimal control theory, where state following (StaF) local approximations were leveraged to reduce the computational demand associated with the generation of an approximate online controller.

**My current research** is focused on the study of system identification methods for nonlinear dynamical systems. This study leverages the concept of occupation kernels and their interactions with Liouville operators (i.e. the generator for the Koopman operator). This includes parameter identification methods as well as the dynamic mode decomposition of continuous-time nonlinear dynamical systems.

My full CV may be found here.