Topic: random matrices

Vijay Balasubramanian connects quantum chaos with the complexity of time evolution. One approach bounds the smallest circuit needed to simulate physical dynamics; another measures how quickly and ergodically a state explores its accessible Hilbert space. Examples from spin chains, billiards, many-body systems and random matrices distinguish chaotic and integrable behaviour. Applications address geometric conjectures for complexity in quantum gravity and possible failure of effective field theory near spacelike singularities.

Joel Tropp studies structured dimension reduction through the injectivity of random maps, motivated by fast low-rank approximation and least-squares regression. This viewpoint sharpens guarantees for sparse maps and gives exponential improvements for tensor-product dimension reduction. Experiments assess the resulting structured random matrices on synthetic problems and scientific applications. Joint work with Chris Camaño, Ethan Epperly, and Raphael Meyer, available as arXiv:2508.21189.