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

Caleb Ashley博士被授予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)，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“Anosov表示的相关函数的幽灵代数”的研究项目。项目活动将在主办机构波士顿学院进行，在马丁·布里奇曼教授的指导下进行。该项目将重点研究布里奇曼-拉布里定义的阿诺索夫表示的关联函数的幽灵代数领域，使用测地线分层和测地线洋流。PI将致力于将这些结构与Fock-Goncherov意义下的正性联系起来的基本问题，以及诸如三角函数等更高循环电流的凸性问题。作为西蒙斯·劳费尔数学科学研究所非洲侨民联合数学讲习班的主任之一，国际和平协会将参与国家范围内的多样性、公平和包容性努力。此外，PI计划指导未被充分代表的学生，并扩大波士顿大学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的法定使命，并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，被认为值得支持。

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.