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SUMMARY:Daniel Glasscock (University of Massachusetts\, Lowell)
DTSTART:20200604T173000Z
DTEND:20200604T175500Z
DTSTAMP:20260423T011320Z
UID:CANT2020/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/50/
 ">Uniformity in the dimension of sumsets of $p$- and $q$-invariant sets\, 
 with applications in the integers</a>\nby Daniel Glasscock (University of 
 Massachusetts\, Lowell) as part of Combinatorial and additive number theor
 y (CANT 2021)\n\n\nAbstract\nHarry Furstenberg made a number of conjecture
 s in the 60's and 70Õs seeking \nto make precise the heuristic that there
  is no common structure between digit expansions \nof real numbers in diff
 erent bases.  Recent solutions to his conjectures  concerning the dimensio
 n \nof sumsets and intersections of times $p$- and $q$-invariant sets now 
 shed new light on old problems.  \nIn this talk\, I will explain how to us
 e tools from fractal geometry and uniform distribution to get \nuniform es
 timates on the Hausdorff dimension of sumsets of times $p$- and $q$-invari
 ant sets.  \nI will explain how these uniform estimates lead to applicatio
 ns in the integers: the dimension \nof a sumset of a p-invariant set and a
  q-invariant set in the integers is as large as it can be.  \n\nThis talk 
 is based on joint work with Joel Moreira and Florian Richter.\n
LOCATION:https://researchseminars.org/talk/CANT2020/50/
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