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SUMMARY:Sascha Troscheit
DTSTART:20210305T091500Z
DTEND:20210305T104500Z
DTSTAMP:20260423T021753Z
UID:DSSUJ/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DSSUJ/21/">A
  dimension theory approach to embeddings in random geometry</a>\nby Sascha
  Troscheit as part of Dynamical systems seminar at the Jagiellonian Univer
 sity\n\nLecture held in 1016.\n\nAbstract\nThe continuum random tree and B
 rownian map are important\nmetric spaces in probability theory and represe
 nt the "typical" tree\nand metric on the sphere\, respectively. The Browni
 an map in particular\nis linked to Liouville Quantum Gravity but the exact
  nature of the\ncorrespondence is unknown.\nIn this talk I will explain a 
 fairly dynamical construction of these\nspaces and show how recent advance
 s in the dimension theory of\nself-similar sets can be used to shed light 
 on general embedding\nproblems. In particular\, I will show that the Assou
 ad dimension of\nthese metric spaces is infinite and show how this restric
 ts the nature\nof embeddings. Time permitting\, I will also indicate how t
 he\nconstruction of continuum trees may be used to analyse highly singular
 \nfunctions such as the Weierstrass-type functions.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/21/
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