John Wiltshire-Gordan

Title: Automatic Functoriality

Abstract: The best constructions in algebra are functorial. As a basic example, suppose you have code that computes the kernel and cokernel of a map. This is great as long as you want individual kernels and cokernels. However, if you have a commuting square of modules, then the two vertical maps induce maps on the kernels and cokernels of the horizontal maps. So you need to implement commuting squares, and then compute the induced maps on ker and coker. But then you realize: a map of commuting squares (a commuting cube) gives rise to a commuting square of kernels! ---and then to a map on cokernels, perhaps, and finally to a single kernel---and therefore you need commuting cubes as well... In this talk, we explain a way to avoid this problem, making constructions automatically functorial using matrices over a category.

Speaker #2

Title and Abstract TBD

Description: TBD

Christine Berkesch Zamaere

Title: Free complexes on smooth toric varieties

Abstract: Free resolutions have been a key part of using homological algebra to compute and characterize geometric invariants over projective space. Over more general smooth toric varieties, this is not the case. We will discuss the another family of complexes, called virtual resolutions, which appear to play the role of free resolutions in this setting. This is joint work with Daniel Erman and Gregory G. Smith.

Christine Berkesch Zamaere, Rachel Davis, and Dave Swinarski

Description: This panel will be an opportunity for grads and others to ask questions about different types of jobs, including postdocs and academic jobs with various different balances between research and teaching.