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），以开展与扩大STEM中代表性不足的群体参与有关的研究，教育和活动计划。该奖学金支持题为“阿诺索夫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，由Martin Bridgeman教授指导。该项目将重点研究由Bridgeman-Labourie定义的Anosov表示的相关函数的鬼代数领域，使用测地线分层和测地线电流。PI将研究将这些结构与Fock-Goncherov意义上的正性联系起来的基本问题，以及高循环电流（如三角形函数）的凸性问题。作为西蒙斯·劳弗数学科学研究所非洲侨民联合数学研讨会的主任之一，PI将参与全国范围内的多样性、公平、包容工作。此外，PI计划指导代表性不足的学生，并扩大波士顿学院实验数学和机器学习实验室的培训和推广工作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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. 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.