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SUMMARY:The Point-to-Set Principle in Metric Spaces and Complexity Classes
  - Neil Lutz (Swarthmore College\, University of Pennsylvania)
DTSTART:20220607T090000Z
DTEND:20220607T100000Z
UID:TALK174794@talks.cam.ac.uk
DESCRIPTION:The Point-to-Set Principle\, which relates the theory of algor
 ithmic information to fractal geometric dimensions\, has been a recent ave
 nue for applications of computability theory to geometric measure theory\,
  primarily in Euclidean spaces. In this talk\, I will describe two ways th
 at the reach of this principle has been extended. First\, it has instances
  in all separable metric spaces and with respect to more general gauges\, 
 permitting a point-to-set analysis of hyperspaces of compact sets\, for ex
 ample. Second\, it has resource-bounded instances that can be used to expl
 ore the fractal structure of complexity classes. Joint work with Jack H. L
 utz and Elvira Mayordomo.
LOCATION:Seminar Room 1\, Newton Institute
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