This month, several experts in frame theory will be visiting my department, and so Matt Fickus and I decided to organize a workshop in the style of AIM. Considering the recent progress we’ve made on equiangular tight frames (ETFs) — namely, one, two, three, and four — we are hoping this workshop will spur further progress in this area. To kick off the month, I asked a few people to prepare hour-long chalk talks, and what follows are the extended abstracts:

**1. Introduction to ETFs (Dustin G. Mixon)**

Given a -dimensional Hilbert space space and a positive integer , we are interested in packing lines through the origin so that the interior angle between any two is as large as possible. It is convenient to represent each line by a unit vector that spans the line, and in doing so, the problem amounts to finding unit vectors that minimize * coherence*:

This minimization amounts to a nonconvex optimization problem. To construct provably optimal packings, one must prove a lower bound on for a given and spatial dimension , and then construct an ensemble which meets equality in that bound. To date, we know of three bounds that are sharp: