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SUMMARY:Generalizing a question of Gromov\, Part II - Johanna Franklin (Ho
 fstra University\, None / Other)
DTSTART:20220609T150000Z
DTEND:20220609T160000Z
UID:TALK174836@talks.cam.ac.uk
DESCRIPTION:This talk is Part II of an account of joint work with Meng-Che
  (Turbo) Ho and Julia Knight on the typicality of groups. In Part I\, Juli
 a Knight presented Gromov's question about groups that inspired this work 
 and its extension to algebraic varieties in general and gave some examples
  of behaviors that we encountered under various assumptions. In this talk\
 , l discuss general conditions that imply some of the behaviors discussed 
 in these examples. Our primary general result states that for a commutativ
 e generalized bijective variety and presentations with a single generator 
 and single identity\, the zero-one law holds and\, furthermore\, that the 
 sentences with density 1 are those true in the free structure. The proof o
 f this result requires a specialized version of Gaifman's Locality Theorem
  that enables us to get a better bound on the complexity of the formulas o
 f interest to us\; I will sketch a proof of this version that uses saturat
 ion and then discuss the proof of our general result.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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