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SUMMARY:Generalizations and Applications of the Lovász theta number
DTSTART:20250513T120000Z
DTEND:20250513T140000Z
DTSTAMP:20260424T055200Z
UID:indico-event-14327@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frank Vallentin (U. Cologne)\n\nThe Lovász theta nu
 mber of a graph\, originally introduced to determine the Shannon capacity 
 of the pentagon\, has been a source of inspiration for everyone working in
  the area of semidefinite programming (linear optimization over the convex
  cone of positive semidefinite matrices). By Lovász's sandwich theorem\, 
 the theta number is sandwiched between the independence number of the grap
 h and the chromatic number of the complementary graph.\nIn the first part 
 of the talk\, I will discuss strengthenings and applications in coding the
 ory and discrete geometry of the Lovász theta number. In concrete applica
 tions\, harmonic analysis will be key to performing explicit computations.
 \nIn the second part of the talk (based on joint work with Davi Castro-Sil
 va\, Fernando M. de Oliveira Filho\, and Lucas Slot)\, I will show how one
  can recursively define a Lovász theta number for uniform hypergraphs. In
  particular\, I will illustrate the use of our new definition by giving a 
 proof of Mantel's theorem about triangle-free sets in graphs\, and by prov
 iding upper bounds for the independence ratio of triangle-avoiding sets in
  the binary Hamming cube\, as well as for simplex-avoiding sets on the uni
 t sphere and in Euclidean space.\n\nhttps://indico.math.cnrs.fr/event/1432
 7/
LOCATION:Salle J. Cavailles (1R2-132) (IMT)
URL:https://indico.math.cnrs.fr/event/14327/
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