Date/Time : 01 Jan 1970 14:00
Venue : via Zoom
Speaker : Zilin Jiang, Arizona State University

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https://nus-sg.zoom.us/j/81639604748?pwd=UXZXTnhwZHRmQTFrZEs0VEtWYjRVUT09

Meeting ID: 816 3960 4748
Passcode: 23571113

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 and 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 equiangular case, that is β = -α, 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 (1 – α)/(β-α) < 2.0198. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.

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