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SUMMARY:Tatiana Smirnova-Nagnibeda (University of Geneva)
DTSTART:20200416T210000Z
DTEND:20200416T220000Z
DTSTAMP:20260404T111324Z
UID:NYGroupTheory/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NYGro
 upTheory/1/">Spectra of laplacians on Cayley and Schreier graphs</a>\nby T
 atiana Smirnova-Nagnibeda (University of Geneva) as part of New York group
  theory seminar\n\n\nAbstract\nWe are interested in  Laplacians on graphs 
 associated with finitely generated groups: Cayley graphs and\, more genera
 lly\, Schreier graphs corresponding to some natural group actions. The spe
 ctrum of such an operator is a compact subset of the closed interval [-1\,
 1]\, but not much more can be said about it in general.\nWe will discuss v
 arious techniques that allow to construct examples with different types of
  spectra -- connected\, union of two intervals\, totally disconnected  -- 
 and with various types of spectral measure. The problem of spectral rigidi
 ty will also be addressed.\n
LOCATION:https://stable.researchseminars.org/talk/NYGroupTheory/1/
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SUMMARY:Frank Wagner (Vanderbilt University)
DTSTART:20200423T210000Z
DTEND:20200423T220000Z
DTSTAMP:20260404T111324Z
UID:NYGroupTheory/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NYGro
 upTheory/2/">Torsion subgroups of groups with cubic Dehn function</a>\nby 
 Frank Wagner (Vanderbilt University) as part of New York group theory semi
 nar\n\n\nAbstract\nThe Dehn function of a finitely presented group\, first
  introduced by Gromov\, is a useful invariant that is closely related to t
 he solvability of the group’s word problem. It is well-known that a fini
 tely presented group is word hyperbolic if and only if it has sub-quadrati
 c (and thus linear) Dehn function. A result of Ghys and de la Harpe states
  that no word hyperbolic group can have a (finitely generated) infinite to
 rsion subgroup. We show that the same does not hold for finitely presented
  groups with Dehn function as small as cubic. In particular\, for every $m
  \\geq 2$ and sufficiently large odd integer $n$\, there exists an embeddi
 ng of the free Burnside group $B(m\,n)$ into a finitely presented group wi
 th cubic Dehn function.\n
LOCATION:https://stable.researchseminars.org/talk/NYGroupTheory/2/
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SUMMARY:Alexander Hulpke (Colorado State University)
DTSTART:20200430T210000Z
DTEND:20200430T220000Z
DTSTAMP:20260404T111324Z
UID:NYGroupTheory/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NYGro
 upTheory/3/">Index computations in arithmetic groups</a>\nby Alexander Hul
 pke (Colorado State University) as part of New York group theory seminar\n
 \n\nAbstract\nThe question whether a subgroup\, given by generators\, has 
 finite (and then which) index is a natural question in group theory. Unfor
 tunately\, for natural groups such as $\\operatorname{SL}_n(\\mathbb{Z})$ 
 and $\\operatorname{Sp}_{2n}(\\mathbb{Z})$\, this question cannot have a g
 eneral algorithmic solution. Nevertheless it is often possible to determin
 e this information in many cases using a computer.\n\nI will describe some
  approaches to this problem and illustrate these in examples.\nThis is joi
 nt work with Alla Detinko (Hull) and Dane Flannery (Galway).\n
LOCATION:https://stable.researchseminars.org/talk/NYGroupTheory/3/
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