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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-208
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:NOÉ DE RANCOURT \, UNIVERSITÉ DE LILLE\n\n_Big Ramsey degrees
  of metric structures_\n\nDistortion problems\, from Banach space geometry
 \, ask about the\npossibility of distorting the norm of a Banach space in 
 a significant\nway on all of its subspaces. Big Ramsey degree problems\, f
 rom\ncombinatorics\, are about proving weak analogues of the infinite Rams
 ey\ntheorem in structures such as hypergraphs\, partially ordered sets\,\n
 etc. Those two topics\, coming back to the seventies\, have quite\ndisjoin
 t motivations but share a surprisingly similar flavour. In a\nongoing work
  with Tristan Bice\, Jan Hubička and Matěj Konečný\, as\na step toward
 s the unification of those two topics\, we developped an\nanalogue of big 
 Ramsey degrees adapted to the study of metric\nstructures (metric spaces\,
  Banach spaces...). Our theory allows us to\nassociate to certain metric s
 tructures a sequence of compact metric\nspaces quantifying their default o
 f Ramseyness. In this talk\, I'll\npresent our theory and its motivations 
 and illustrate it on the\nexamples of the Banach space $\\ell_\\infty$ and
  the Urysohn sphere. If\ntime permits\, links with topological dynamics wi
 ll also be discussed.\n\nQNC 1507 or Join on Zoom\n[https://uwaterloo.zoom
 .us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09]
DTSTAMP:20260501T182921Z
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