[DMO] Giulia Montagna: Equiangular lines with a fixed angle

03 March 2023 14:00 till 15:00 - Location: EMCS Lecture Hall J, LH.01.430 | Add to my calendar

A set of lines through the origin in R^d is called equiangular when any two lines from the set share the same angle. Let N_α(d) denote the maximum number of lines through the origin in R^d with pairwise common angle arccos α. A few years ago Jiang, Tidor, Yao, Zhang and Zhao solved the problem of determining N_α(d) in large enough dimensions. Their result is as follows. Let k denote the minimum number of vertices in a graph whose adjacency matrix has spectral radius exactly (1−α)/(2α). If k exists, then N_α(d) = ⌊k(d-1)/(k-1)⌋ for all sufficiently large d. Otherwise, N_α(d) = d + o(d). In this talk I will present the proof of this result.