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

博士后奖学金：MPS-Ascend：非平稳动力系统的平衡态

• 批准号: 2316687
• 负责人: Gregory Hemenway
• 金额: $ 30万
• 依托单位: Hemenway, Gregory
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316687&HistoricalAwards=false
• 关键词: Postdoctoral; Fellowship; MPS; Ascend; Equilibrium

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.

Gregory Hemenway 博士被授予美国国家科学基金会数学和物理科学提升博士后研究奖学金 (NSF MPS-Ascend)，用于开展与扩大 STEM 代表性不足群体的参与相关的研究、教育和活动计划。该奖学金支持题为“非平稳动力系统的平衡状态”的研究项目。该项目活动将在主办机构俄亥俄州立大学进行，并在 Daniel Thompson 博士的指导下进行。许多现实世界的系统表现出混乱的行为：测量中的小误差会迅速复合，并使对系统未来状态的预测变得毫无价值。我们可以将此类系统视为随机过程，并使用遍历理论研究它们的渐近行为。稳态动力学得到了很好的研究，其中迭代相同的映射以获得渐近行为的结果。在他的博士论文中，海明威博士使用热力学形式主义技术来研究表现出非平稳行为的混沌系统。在该项目期间，Hemenway 博士将继续发展他的研究计划，研究高维空间上的扩展映射之间的共轭性、用于表征偏斜乘积条件测量的几何方法，以及非平稳结果在 beta 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，Hemenway 博士致力于帮助缩小少数族裔在研究层面参与 STEM 的差距。该项目的更广泛影响将包括参与旨在大学一级招募和保留少数族裔的计划、研讨会和活动。此次参与将涉及指导、教学和数学相关活动的发展等方面，以加强和激发学生的数学能力。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。