The Mathematical Sciences Institute, the ANU Film Group and the Embassy of the Republic of Poland in Canberra are delighted to present the screening of Adventures of a Mathematician. Light refreshments will be served along with short speeches from organisers before the movie starts. After migrating to the U.S. in the late 1930s, Polish-Jewish mathematician Stanislaw ‘Stan’ Ulam (Philippe Tlokinski) is offered an opportunity to work on a top-secret project in New Mexico. Ulam and his new wife (Esther Garrel) move to the newly-built town of Los Alamos, where Ulam becomes part of a team of brilliant young immigrant scientists whose work leads to the creation of the hydrogen bomb. But despite his success, Ulam finds himself wracked with guilt over the family he left behind in Poland.

Abstract

Someone told me once that Gaussian elimination is the one thing a mathematician learns as an undergrad and then never really uses in research. This talk is about proving this is false. I will first introduce a homological algebra version of Gaussian elimination, due to Bar-Natan, which can be used to simplify complexes (e.g., chain complexes) arising in many areas of mathematics such as algebraic topology and representation theory. Then, following Sköldberg, I will explain how to interpret this operation as a "collapse" in the sense of Forman's discrete Morse theory. Finally I will describe an application of this method to Rouquier complexes, certain interesting objects upgrading the braid group to a category.

Abstract 

Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed using the formalism of spherical functors. I will introduce this, and discuss work in progress on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal.

Abstract: We consider the Klein-Gordon equation on Minkowski space with a class of space-time potentials that decay sufficiently fast in spatial directions and approach a limiting potential as t → ∞. Building on previous work of Vasy for many-body scattering problems, we show that the Klein-Gordon operator admits a description as a non-elliptic Fredholm operator as a map between anisotropic Sobolev spaces. The talk is based on joint work with Dean Baskin and Jesse Gell-Redman