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One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.

Categorical symplectic geometry studies an invariant of symplectic manifolds called the "Fukaya (A-infinity) category", which consists of the Lagrangian submanifolds and a symplectically-robust intersection theory of these Lagrangians.  Over the last two decades the Fukaya category has emerged as a powerful tool: for instance, it has produced inroads to Arnol'd's Nearby Lagrangians Conjecture, and it allowed Kontsevich to formulate the the Homological Mirror Symmetry conjecture.

In this talk I will describe a project, joint with Satyan Devadoss, Stefan Forcey, and Katrin Wehrheim, which attempts to relate the Fukaya categories of different symplectic manifolds via a notion of functoriality.  After mentioning some analytic results about the singular quilts necessary for this construction, I will describe the combinatorial component: with Devadoss and Forcey we are constructing a family of polytopes that specialize to the associahedra in two different ways, and can be thought of as the 2-categorical version of associahedra.

Generation of accurate mock observations tailored specifically to upcoming surveys such as Advanced ACT, CHIME, and LSST is a key technical challenge in cosmology. Traditional approaches involving N-body simulation are fraught with difficulties due to increasingly large survey volumes and depths. Typically, statistical ensembles can only be realized for a few carefully-chosen parameters, limiting exploration to a significantly restricted cosmological model space. We have developed a new massively parallel algorithm to generate accurate halo masses and positions in a fraction (~1e-3 to 1e-2) of the time taken by N-body simulations. I will present a suite of simulated full sky cluster Sunyaev-Zel’dovich maps that have been produced with this approach, and describe the types of virtual large scale structure observations that are now within reach in the coming years.