Federal Grant Award Summary

The University of Chicago received a $257,479 CAREER (Faculty Early Career Development) Project Grant from the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026, through June 30, 2031. The award funds fundamental research investigating the geometric foundations of stochastic dynamics across four interconnected research directions: developing coarse graining techniques to characterize fractal structures in critical stochastic systems such as two-dimensional stochastic heat flow and directed random polymers; establishing probabilistic frameworks for symplectic geometry in quantum Teichmüller space through semiclassical analysis of Liouville quantum gravity; formulating entropy-based selection principles in optimal transport on Riemannian and Lorentzian manifolds with applications to gravitational physics; and building rigorous theory for convergence of interacting particle dynamics underlying generative artificial intelligence algorithms.

Beyond core research deliverables, the award supports significant broader impact activities including mentorship of students across multiple institutions, development of new graduate courses at the intersection of probability and machine learning, and co-organization of research programs and workshops at national mathematics institutes. The project addresses fundamental gaps in understanding the interplay between randomness, geometry, and dynamics across multiple scales and disciplines, with implications spanning mathematical sciences, physics, and computational methods.