# Algebra Geometry Seminar: Leveraging Symmetry for Optimal Line Packings

**Author: Lona**

**Author: Lona**

Speaker: Joey Iverson (ISU)

Abstract:

How can we arrange lines to pass through the origin without creating sharp angles? This question arises in applications such as compressed sensing, wireless communication, and quantum information theory. For a fixed number of lines in a fixed dimension, an “optimal line packing” is one in which the sharpest angle is made as wide as possible. Examples include the 6 lines in R^{3} that connect antipodes of a 20-sided die, and the 3 lines in R^{2} that arise from the Mercedes-Benz logo. Many of the known optimal line packings feature remarkable symmetry. In particular, they arise as orbits of unitary representations of finite groups. In this talk, we investigate the structure of such symmetric line systems, and we demonstrate a method to recover the lines from their automorphism group. Our work leads to a partial classification of doubly transitive line packings.

Based on joint work with John Jasper and Dustin G. Mixon.