The National Science Foundation (NSF) awarded a $340,214 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of California, San Diego (UCSD) for a research project titled "Stationary Random Systems via an Asymptotic Approach." The grant, effective from July 15, 2024 to June 30, 2027, supports fundamental research focused on three key areas: 1) the Furstenberg entropy realization problem for classical matrix groups, 2) the longstanding amenability problem of iterated monodromy groups originating from conformal dynamics, and 3) a new procedure called "random walk cocycle sampling limit" and its potential applications. The project aims to advance the understanding of stationary random networks and random walks on groups, utilizing entropy theory as the underlying tool. The research outcomes are expected to provide insights into the interplay between rigidity and flexibility in stationary random systems and shed light on critical cases in conformal geometry. This award reflects NSF's mission to strengthen the nation's scientific enterprise by supporting cutting-edge mathematical and physical sciences research with potential for significant scientific and technological impacts.
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