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1-2-3 Seminar: Hyperplanes, Posets, and Cohomology, Oh My!

Cameron Wright, University of Washington
Friday, May 3, 2024 - 2:30pm to 3:30pm
PDL C-401

In this talk we examine some aspects of the modern theory of hyperplane arrangements, a theory which stars an interesting interplay between combinatorics and topology. Over the course of the talk, we will familiarize ourselves with two main characters associated with any arrangement: the intersection poset and the complex complement. The former is a combinatorial object associated to the arrangement and the latter is an interesting topological space given by taking the complement of the arrangement in a complex vector space. Over the reals, the complement of an arrangement consists of finitely many contractible polyhedra; over the complex numbers, the complement of an arrangement is connected in general and has nontrivial topology. We shall see that several interesting topological invariants of the complex complement are determined by combinatorial invariants associated to the arrangement.

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