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

Gregory Hemenway博士被授予国家科学基金会数学和物理科学上升博士后研究奖学金(NSF MPS-Ascend)，以开展一项与扩大STEM中代表性不足群体的参与相关的研究、教育和活动。该奖学金资助了题为“非定常动力系统的平衡态”的研究项目。该项目的活动将在主办机构俄亥俄州立大学进行，由丹尼尔·汤普森博士指导。许多真实世界的系统表现出混乱的行为：测量中的小误差迅速合成，使对系统未来状态的预测变得毫无价值。我们可以将这类系统视为随机过程，并利用遍历理论研究其渐近行为。深入研究了迭代相同映射以获得渐近行为结果的平稳动力学。在他的博士论文中，海门威博士使用热力学形式论中的技术来研究表现出非平稳行为的混沌系统。在这个项目中，海门威博士将继续发展他的研究计划，他将研究高维空间上的扩张映射之间的共轭关系，刻画斜积的条件测度的几何方法，以及非平稳结果在贝塔变换和台球等有趣系统中的应用。作为一名非裔美国数学家，海门威博士致力于在研究层面帮助弥合少数族裔参与STEM的差距。该项目的更广泛影响将包括参与迎合在大学一级招募和留住少数族裔的方案、研讨会和活动。这个奖项反映了NSF的法定使命，通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为是值得支持的。

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.