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UID:69f7385a17cd0
DTSTART;TZID=America/Toronto:20260115T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-defence-0
SUMMARY:PhD. Defence
CLASS:PUBLIC
DESCRIPTION:JOAQUIN G. PRANDI\, UNIVERSITY OF WATERLOO\n\n_Iterated Functi
 on Systems and the Local Dimension of Measures_\n\nGiven an iterated funct
 ion system S in R^d\, with full support and such\nthat the rotation in it 
 fixed the hypercube [-1/2\,1/2]^d \, then S\nsatisfies the weak separation
  condition if and only if it satisfies\nthe generalized finite-type condit
 ion. With this in mind\, we extend\nthe notion of net intervals from R to 
 R^d. We also use net intervals\nto calculate the local dimension of a self
 -similar measure with the\nfinite-type condition and full support.\n\nWe s
 tudy the local dimension of the convolution of two measures. We\ngive cond
 itions for bounding the local dimension of the convolution on\nthe basis o
 f the local dimension of one of them. Moreover\, we give a\nformula for th
 e local dimension of some special points in the support\nof the convolutio
 n.\n\nWe study the local dimension of the addition of two measures. We giv
 e\nan exact formula for the lower local dimension of the addition based\no
 n the local dimension of the two added measures. We give an upper\nbound t
 o the upper local dimension of the addition of two measures. We\nexplore t
 he special case where the two measures satisfy the convex\nadditive finite
 -type condition that we introduce.\n\nWe introduce the notion of graph ite
 rated function system. We show\nthat we can always associate a self simila
 r to the graph iterated\nfunction system.\n\nMC 5417\n\n 
DTSTAMP:20260503T115818Z
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