Equiangular lines and spherical codes in Euclidean spaces

Seminar: 
Robinson Lectures
Event time: 
Thursday, February 2, 2017 - 11:30am to 12:30pm
Location: 
LOM 205
Speaker: 
Benjamin Sudakov
Speaker affiliation: 
EtH Zurich
Event description: 

A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in Rn was extensively studied for the last 70 years. Answering a question of Lemmens and Seidel from 1973, in this talk we show that for every fixed angle θ and sufficiently large n there are at most 2n2 lines in Rn with common angle θ.
Moreover, this is achievable only when θ=arccos13.
Various extensions of this result to the more general settings of lines with k fixed angles and of spherical codes will be discussed as well. Joint work with I. Balla, F. Drexler and P. Keevash.