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SUMMARY:Random walks on homogeneous spaces\, Spectral Gaps\, and Khintchin
 e's theorem on fractals
DTSTART:20211007T131500
DTEND:20211007T150000
DTSTAMP:20260916T055722Z
UID:ec009d94a6fe16f38010863ba4d01fdd4af17006dd9dc8815b70157f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Manuel Luethi (EPFL)\nKhintchine's theorem in Diophantine appr
 oximation gives a zero one law describing the approximability of typical p
 oints by rational points. In 1984\, Mahler asked how well points on the mi
 ddle third Cantor set can be approximated. His question fits into an attem
 pt to determine conditions under which subsets of Euclidean space inherit 
 the Diophantine properties of the ambient space. I will discuss a complete
  analogue of the theorem of Khintchine for certain fractal measures which 
 was recently obtained in collaboration with Osama Khalil. Our results hold
  for fractals generated by rational similarities of Euclidean space that h
 ave sufficiently small Hausdorff co-dimension. The main ingredient to the 
 proof is an effective equidistribution theorem for associated fractal meas
 ures on the space of unimodular lattices. The latter is established using 
 a spectral gap property of a type of Markov operators associated with an S
 -arithmetic random walk related to the generating similarities.
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CONFIRMED
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