Much of the important combinatorial information about an arrangement of hyperplanes can be understood by studying the cohomology ring of its complement. Given an arrangement with a group action G, a fundamental but difficult question is: how does one describe the G-representations on the (graded pieces of the) cohomology ring of its complement? In this talk, I will discuss some methods of answering this question—computational and otherwise—as well as challenges that arise. This is partially based on joint work with Megan Chang-Lee and Trevor Karn.
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