Postdoctoral Fellowship: MPS-Ascend: The Ghost Algebra for Correlation Functions & Convexity of Anosov Representations

博士后奖学金：MPS-Ascend：相关函数的幽灵代数

• 批准号: 2316685
• 负责人: Caleb Ashley
• 金额: $ 30万
• 依托单位: Ashley, Caleb J
• 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: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316685&HistoricalAwards=false
• 关键词: Postdoctoral; Fellowship; MPS; Ascend; Ghost

Dr. Caleb Ashley 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 "The ghost algebra for correlation functions of Anosov representations." The project activities will be conducted at the host institution, Boston College, under the mentorship of Professor Martin Bridgeman.This project will focus on research in the area of the ghost algebra for correlation functions of Anosov representations, as defined by Bridgeman-Labourie, using geodesic laminations and geodesic currents. The PI will work on the fundamental question of relating these structures to positivity in the sense of Fock-Goncherov and on the question of convexity for higher cyclic currents such as triangle functions. In the role as one of the directors of the African Diaspora Joint Mathematics Workshop at the Simons Laufer Mathematical Sciences Institute, the PI will participate in Diversity, Equity, Inclusion efforts on the national scale. Additionally, the PI plans to mentor underrepresented students and expand the training and outreach efforts of the Experimental Mathematics and Machine Learning Laboratory at Boston College.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.

卡莱布·阿什利（Caleb Ashley）博士被授予国家科学基金会的数学和物理科学，上升博士后研究奖学金（NSF MPS-ASCEND），以进行研究，教育和活动计划，与STEM中代表性不足的团体扩大参与有关的活动。该奖学金支持题为“ Anosov表示相关函数的幽灵代数”的研究项目。该项目活动将在马丁·布里奇曼教授的指导下在波士顿学院的东道国机构进行。本项目将重点介绍幽灵代数领域的研究，用于使用Bridgeman-Labourie定义的Anosov代表的相关功能，该项目使用地质层压层和地球层流。 PI将在Fock-Goncherov的意义上将这些结构与积极性联系起来的基本问题，以及对于较高的环状电流（例如三角形功能）的凸性问题。作为西蒙斯·劳弗（Simons Laufer）数学科学研究所的非洲侨民联合数学研讨会的董事之一，PI将在国家规模上参与多样性，公平，包容性工作。此外，PI计划指导代表人数不足，并扩大波士顿学院实验数学和机器学习实验室的培训和外展工作。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来通过评估来获得支持的。