This training program is specifically designed for graduate students and recent PhDs in mathematics or related fields, who are looking to transition to work in the information security industry after graduation.

The Bernstein-Sato polynomial (and its roots) are important invariants of hypersurface singularities. It is a Rosetta Stone: it seems most singularity data lies within, if only one could decode it. Unfortunately, after 50 years actual computations remain scarce. I will give a formula for the roots of Bernstein-Sato polynomials of hyperplane arrangements in three variables. It turns out all but one root is determined by the combinatorics, and the outlier root is determined by simple algebraic data. Time permitting I will connect this non-combinatorial root to the realization space of the underlying matroid.

For a compact surface S, $MCG(S) = Homeo(S)/Homeo_0(S)$ is a group well-studied and loved by many, but especially by geometric group theorists because it is finitely generated, and hence has a coarse geometry coming from its Cayley graph. When S is big (infinite-type), $MCG(S)$ is Polish and no longer discrete, but following the work of Rosendal and Mann-Rafi, we can still define a coarse geometry and a Cayley graph. In ongoing work with Schaffer-Cohen—Verberne and Qing—Rafi, we can show that for some surfaces, $MCG(S)$ is non-elementary $\delta$-hyperbolic, and some have infinite coarse rank. If you like surfaces, geometry, topology, and Polish groups, come by!

TBA