Gravitational collapse of matter clouds is a fundamental process in astrophysics, cosmology, and black hole physics today.

We study the size blow-up that is necessary to convert an algebraic circuit of constant product-depth D+1 to one of product-depth D in the multilinear setting.

Given a graph $G$, let $\mathbb{P}_G$ denote the cone of positive semidefinite (psd) matrices, with non-negative entries, and zeros according to $G$. Which powers preserve psd-ness when applied entrywise to all matrices in $\mathbb{P}_G$?

We study the logistics system of eukaryotic cells, whose warehouses are micron-scale "organelles" and whose trucks are 10-nanometer-scale "vesicles". Organelles form the nodes and vesicle fluxes form the edges of a transport graph.

In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities.