Recorded 11 February 2025. Sarah Brauner of Brown University presents "Symmetries of rings from hyperplane arrangements" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: 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. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/