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SUMMARY:David Hume (University of Birmingham)
DTSTART:20260514T123000Z
DTEND:20260514T133000Z
DTSTAMP:20260623T074559Z
UID:GaTO/146
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/146/">T
 he Poincaré critical exponent</a>\nby David Hume (University of Birmingha
 m) as part of Geometry and topology online\n\nLecture held in Room B3.02 i
 n the Zeeman Building\, University of Warwick.\n\nAbstract\nThe Poincaré 
 critical exponent (PCE) assigns to each bounded degree graph X a value p_X
  ∈ [1\,+∞]. PCEs satisfy a strong monotonicity property: whenever ther
 e is a Lipschitz\, bounded-to-one map X-> Y\, it holds p_X ≤ p_Y. In par
 ticular\, if X and Y are Cayley graphs of finitely generated groups H and 
 G\, and H is quasi-isometric to a subgroup of G\, then p_X≤ p_Y.\n\nWhen
  X is the Cayley graph of a virtually nilpotent group G\, p_X is the degre
 e of polynomial growth\, and for many hyperbolic groups p_X is the conform
 al dimension of the boundary of G.\n\nIn this talk I will define PCEs\, ex
 plain some of their properties and highlight many interesting open questio
 ns.\n
LOCATION:https://researchseminars.org/talk/GaTO/146/
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