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SUMMARY:Yufei Zhao (Massachusetts Institute of Technology)
DTSTART:20200806T020000Z
DTEND:20200806T030000Z
DTSTAMP:20260423T021020Z
UID:SCMSComb/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/7/"
 >Equiangular lines\, spherical two-distance sets\, and spectral graph theo
 ry</a>\nby Yufei Zhao (Massachusetts Institute of Technology) as part of S
 CMS Combinatorics Seminar\n\n\nAbstract\nSolving a longstanding problem on
  equiangular lines\, we determine\, for each given fixed angle and in all 
 sufficiently large dimensions\, the maximum number of lines pairwise separ
 ated by the given angle. The answer is expressed in terms of spectral radi
 i of graphs.\n\nGeneralizing to spherical two-distance sets\, we conjectur
 ally relate the problem to a certain eigenvalue problem for signed graphs\
 , and solve it in a number of cases.\n\nA key ingredient is a new result i
 n spectral graph theory: the adjacency matrix of a connected bounded degre
 e graph has sublinear second eigenvalue multiplicity.\n\nJoint work with Z
 ilin Jiang\, Jonathan Tidor\, Yuan Yao\, and Shengtong Zhang (all MIT)\n\n
 password 111317\n
LOCATION:https://researchseminars.org/talk/SCMSComb/7/
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