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SUMMARY:Generalizing a question of Gromov\, Part I - Julia F. Knight (Univ
 ersity of Notre Dame\, None / Other)
DTSTART:20220606T133000Z
DTEND:20220606T143000Z
UID:TALK174785@talks.cam.ac.uk
DESCRIPTION:This talk is Part I of an account of joint work with Johanna F
 ranklin and Meng-Che (Turbo) Ho. &nbsp\;Johanna Franklin's talk is Part II
 . &nbsp\;Gromov asked\, ``What is a typical group?'' &nbsp\;He was thinkin
 g of finitely presented groups\, and he proposed an approach involving lim
 iting density. &nbsp\;In 2013\, I conjectured that for presentations with 
 $n\\geq 2$ generators and a single relator\, the elementary first order se
 ntences true in the typical group are those true in the free group. &nbsp\
 ;The conjecture is still open\, but there are partial positive results by 
 Kharlampovich and Miasnikov\, and by Ho and Logan. &nbsp\;In our joint wor
 k\, Franklin\, Ho\, and I consider other algebraic varieties\, in the sens
 e of universal algebra\, asking the analogue of Gromov's question. &nbsp\;
 We have examples illustrating different possible behaviors. &nbsp\;For var
 ieties with finitely many unary function symbols\, we have a general resul
 t with conditions sufficient to guarantee that the analogue of the conject
 ure holds. &nbsp\;The proof uses a version of Gaifman's Locality Theorem\,
  plus ideas from random group theory. &nbsp\;Part I will describe Gromov's
  original question and its extension to other algebraic varieties\, with s
 ome examples. &nbsp\; &nbsp\; &nbsp\;&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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