BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jonathan Tidor (MIT)
DTSTART:20210215T140000Z
DTEND:20210215T150000Z
DTSTAMP:20260423T021002Z
UID:EPC/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/49/">Equ
 iangular lines with a fixed angle</a>\nby Jonathan Tidor (MIT) as part of 
 Extremal and probabilistic combinatorics webinar\n\n\nAbstract\nA configur
 ation of N lines through the origin in d-dimensional Euclidean space is ca
 lled equiangular if the lines are pairwise separated by the same angle. A 
 natural and long-standing problem in discrete geometry is to determine the
  maximum size of a configuration of equiangular lines in a given dimension
 .\n\nWe determine\, for each fixed angle and in all sufficiently large dim
 ensions\, the maximum number of equiangular lines separated by this given 
 angle. Surprisingly\, this maximum depends on spectral graph theoretic pro
 perties of the fixed angle.\n\nOur proof involves the following novel resu
 lt that seems to be of independent interest: A bounded degree connected gr
 aph has sublinear second eigenvalue multiplicity (that is\, the multiplici
 ty of the second-largest eigenvalue of the adjacency matrix of the graph i
 s sublinear in the number of vertices).\n\nJoint work with Zilin Jiang\, Y
 uan Yao\, Shengtong Zhang\, and Yufei Zhao.\n
LOCATION:https://researchseminars.org/talk/EPC/49/
END:VEVENT
END:VCALENDAR