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DTSTAMP:20261017T160007Z
SUMMARY:Analysis and dynamics seminar
DESCRIPTION:Speaker: Cagri Sert (University of Warwick)\n\nTitle: Projectio
 ns of self-affine fractals\n\nAbstract: I will discuss the extension of Fa
 lconer’s landmark 1988 result — on the Hausdorff dimension of typical
  self-affine fractals — to linear projections of these fractals. The res
 ult uncovers an algebraic structure on the exceptional sets of projections
  in the sense of Marstand projection theorem. Furthermore\, the results c
 omes with various examples of new phenomena that I will mention. This incl
 ude\n\n\n existence of equilibrium states having non-exact dimensional li
 near projections (equilibrium states themselves are exact dimensional by F
 eng)\;\n\n\n\n\nexistence of self-affine fractals in dimensions at least 4
 \, whose set of exceptional\n\nprojections contains higher degree algebrai
 c varieties in Grassmannians (such\n\n\nconstructions are not possible eve
 n in Borel category in dimension 3 by the\n\n\nsolution of a conjecture of
  F\\”{a}ssler-Orponen by Gan et.al.\, nor in any dimension\n\n\nif the l
 inear parts of affinities acts strongly irreducibly on all exterior powers
 \, by Rapaport)\n\n\n\nexistence of self-affine fractals whose sumsets hav
 e lower than expected dimension\n\nwithout satisfying an arithmetic resona
 nce (impossible in dimension 1 by Hochman\,\n\n\nShmerkin\, Peres and in d
 imension 2 by Pyor\\”{a}l\\”{a}).\n\n\n\nJoint work with Ian D. Morris
 .
URL:https://www.imperial.ac.uk/events/189917/analysis-and-dynamics-seminar-
 2/
DTSTART;TZID=Europe/London:20250306T130000
DTEND;TZID=Europe/London:20250306T140000
LOCATION:Room 411\, Huxley Building\, South Kensington Campus\, Imperial Co
 llege London\, London\, SW7 2AZ\, United Kingdom
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