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SUMMARY:Finite reflection groups and graph norms - David Conlon (Universit
 y of Oxford)
DTSTART:20161117T143000Z
DTEND:20161117T153000Z
UID:TALK68665@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:For any given graph H\, we may define a natural corresponding 
 functional ||.||_H. We then say that H is norming if ||.||_H is a semi-nor
 m. A similar notion\n||.||_r(H) is defined by || f ||_r(H) := || | f | ||_
 H and H is said to be weakly norming if ||.||_r(H) is a norm. Classical re
 sults show that weakly norming graphs are necessarily bipartite. In the ot
 her direction\, Hatami showed that even cycles\, complete bipartite graphs
 \, and hypercubes are all weakly norming. Using results from the theory of
  finite reflection groups\, we identify a much larger class of weakly norm
 ing graphs. This result includes all previous examples of weakly norming g
 raphs and adds many more. We also discuss several\napplications of our res
 ults. In particular\, we define and compare a number of generalisations of
  Gowers' octahedral norms and we prove some new instances of Sidorenko's c
 onjecture. Joint work with Joonkyung Lee.\n
LOCATION:MR12
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