R440, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 440室)

Spherical Two-distance Sets and Spectral Theory of Signed Graphs

Zilin Jiang (Massachusetts Institute of Technology)

Abstract:

A set of unit vectors in a Euclidean space is called a spherical two-distance set if the pairwise inner products of these vectors assume only two values α > β. It is known that the maximum size of a spherical two-distance grows quadratically as the dimension of the Euclidean space grows. However when the values α and β are held fixed, a very intricate behavior of the maximum size emerges. Building on our recent resolution in the case of α + β = 0, we make a plausible conjecture which connects this behavior with spectral theory of signed graphs in the regime β < 0 < α, and we confirm this conjecture when α + 2β < 0 or

is 1,

or

.