### Equiangular tight frames from association schemes

- Series
- Analysis Seminar
- Time
- Wednesday, November 9, 2016 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- John Jasper – University of Cincinnati – john.jasper@uc.edu

An
equiangular tight frame (ETF) is a set of unit vectors whose coherence
achieves the Welch bound. Though they arise in many applications, there
are only a
few known methods for constructing ETFs. One of the most popular
classes of ETFs, called harmonic ETFs, is constructed using the
structure of finite abelian groups. In this talk we will discuss a broad
generalization of harmonic ETFs. This generalization allows
us to construct ETFs using many different structures in the place of
abelian groups, including nonabelian groups, Gelfand pairs of finite
groups, and more. We apply this theory to construct an infinite family
of ETFs using the group schemes associated with
certain Suzuki 2-groups. Notably, this is the first known infinite
family of equiangular lines arising from nonabelian groups.