Speaker: Patrick Charbonneau
Abstract. Using mathematical physics tools and methods adapted from the study of spin glasses, a description hard sphere glasses in the high-dimensional limit has recently been conjectured. In addition to providing a reliable framework with which to compare numerical and other experiments, this treatment predicts the existence, deep in the glass phase, of a novel phase transition, a so-called Gardner transition. This transition signals the emergence of a complex landscape composed of a marginally stable hierarchy of sub-basins. In this talk, I will present an overview of our recent theoretical and numerical advances in capturing and characterizing this novel materials feature. I will also discuss some of the key finite-dimensional corrections to this description and their connection to open problems in stochastic topology.