Postdoctoral Fellowship: MPS-Ascend: Equilibrium States for Non-stationary Dynamical Systems

Dr. Gregory Hemenway is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research, education, and activities related to broadening participation by groups underrepresented in STEM. This fellowship supports the research project entitled "Equilibrium States for Non-stationary Dynamical Systems". The project activities will be conducted at the host institution, the Ohio State University, under the mentorship of Dr. Daniel Thompson. Many real-world systems exhibit chaotic behavior: small errors in measurements compound quickly and render predictions of future states of the system worthless. We can view such systems as stochastic processes and study their asymptotic behavior using ergodic theory. Stationary dynamics in which the same map is iterated to obtain results about asymptotic behaviors are well studied. In his doctoral thesis, Dr. Hemenway used techniques from thermodynamic formalism to study chaotic systems that exhibit non-stationary behavior. During this project, Dr. Hemenway will continue to develop his research program as he investigates conjugacies between expanding maps on higher dimensional spaces, geometric approaches for characterizing conditional measures for skew products, and applications of non-stationary results to interesting systems like beta transformations and billiards. As an African American mathematician, Dr. Hemenway is dedicated to helping bridge the gap in minority participation in STEM at the research level. The broader impacts of this project will include participation in programs, workshops, and activities that cater to the recruitment and retention of minorities at the university level. This participation will involve aspects of mentoring, teaching, and the development of math related activities that reinforce and stimulate students' mathematical prowess. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.