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

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.