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

Gregory Hemenway博士被授予美国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），以开展与扩大STEM中代表性不足的群体的参与有关的研究，教育和活动计划。该研究金支持题为“非平稳动力系统的平衡态”的研究项目。项目活动将在主办机构俄亥俄州州立大学进行，由丹尼尔·汤普森博士指导。许多现实世界的系统表现出混乱的行为：测量中的小误差迅速复合，并使对系统未来状态的预测变得毫无价值。我们可以把这样的系统看作随机过程，用遍历理论研究它们的渐近行为。平稳动力学中，相同的映射迭代，以获得有关渐近行为的结果得到了很好的研究。在他的博士论文中，Hemenway博士使用热力学形式主义的技术来研究表现出非稳态行为的混沌系统。Hemenway博士将继续发展他的研究计划，因为他研究了高维空间上扩展映射之间的共轭性，用于表征偏斜产品的条件措施的几何方法，以及非平稳结果在有趣的系统中的应用，如beta变换和台球。作为一名非裔美国数学家，Hemenway博士致力于帮助弥合少数民族参与STEM研究的差距。该项目的更广泛影响将包括参与在大学一级招收和留住少数群体的方案、讲习班和活动。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.