Friday, November 16, 2018 - 15:55 , Location: Skiles 006 , Mark Rudelson , University of Michigan , firstname.lastname@example.org , Organizer: Galyna Livshyts
TBANote the special time!
Wednesday, October 24, 2018 - 12:55 , Location: Skiles 006 , Dmitry Ryabogin , Kent State University , email@example.com , Organizer: Galyna Livshyts
Wednesday, October 10, 2018 - 12:55 , Location: Skiles 006 , Josiah Park , Georgia institute of Technology , firstname.lastname@example.org , Organizer: Galyna Livshyts
It has been known that when an equiangular tight frame (ETF) of size |Φ|=N exists, Φ ⊂ Fd (real or complex), for p > 2 the p-frame potential ∑i ≠ j | < φj, φk > |p achieves its minimum value on an ETF over all N sized collections of vectors. We are interested in minimizing a related quantity: 1/ N2 ∑i, j=1 | < φj, φk > |p . In particular we ask when there exists a configuration of vectors for which this quantity is minimized over all sized subsets of the real or complex sphere of a fixed dimension. Also of interest is the structure of minimizers over all unit vector subsets of Fd of size N. We shall present some results for p in (2, 4) along with numerical results and conjectures. Portions of this talk are based on recent work of D. Bilyk, A. Glazyrin, R. Matzke, and O. Vlasiuk.