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SUMMARY:Tatiana Smirnova-Nagnibeda (University of Geneva)
DTSTART:20200416T210000Z
DTEND:20200416T220000Z
DTSTAMP:20260422T225842Z
UID:NYGroupTheory/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYGroupTheor
 y/1/">Spectra of laplacians on Cayley and Schreier graphs</a>\nby Tatiana 
 Smirnova-Nagnibeda (University of Geneva) as part of New York group theory
  seminar\n\n\nAbstract\nWe are interested in  Laplacians on graphs associa
 ted with finitely generated groups: Cayley graphs and\, more generally\, S
 chreier graphs corresponding to some natural group actions. The spectrum o
 f such an operator is a compact subset of the closed interval [-1\,1]\, bu
 t not much more can be said about it in general.\nWe will discuss various 
 techniques that allow to construct examples with different types of spectr
 a -- connected\, union of two intervals\, totally disconnected  -- and wit
 h various types of spectral measure. The problem of spectral rigidity will
  also be addressed.\n
LOCATION:https://researchseminars.org/talk/NYGroupTheory/1/
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SUMMARY:Frank Wagner (Vanderbilt University)
DTSTART:20200423T210000Z
DTEND:20200423T220000Z
DTSTAMP:20260422T225842Z
UID:NYGroupTheory/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYGroupTheor
 y/2/">Torsion subgroups of groups with cubic Dehn function</a>\nby Frank W
 agner (Vanderbilt University) as part of New York group theory seminar\n\n
 \nAbstract\nThe Dehn function of a finitely presented group\, first introd
 uced by Gromov\, is a useful invariant that is closely related to the solv
 ability of the group’s word problem. It is well-known that a finitely pr
 esented group is word hyperbolic if and only if it has sub-quadratic (and 
 thus linear) Dehn function. A result of Ghys and de la Harpe states that n
 o word hyperbolic group can have a (finitely generated) infinite torsion s
 ubgroup. 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 embedding of t
 he free Burnside group $B(m\,n)$ into a finitely presented group with cubi
 c Dehn function.\n
LOCATION:https://researchseminars.org/talk/NYGroupTheory/2/
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SUMMARY:Alexander Hulpke (Colorado State University)
DTSTART:20200430T210000Z
DTEND:20200430T220000Z
DTSTAMP:20260422T225842Z
UID:NYGroupTheory/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYGroupTheor
 y/3/">Index computations in arithmetic groups</a>\nby Alexander Hulpke (Co
 lorado State University) as part of New York group theory seminar\n\n\nAbs
 tract\nThe question whether a subgroup\, given by generators\, has finite 
 (and then which) index is a natural question in group theory. Unfortunatel
 y\, for natural groups such as $\\operatorname{SL}_n(\\mathbb{Z})$ and $\\
 operatorname{Sp}_{2n}(\\mathbb{Z})$\, this question cannot have a general 
 algorithmic solution. Nevertheless it is often possible to determine this 
 information in many cases using a computer.\n\nI will describe some approa
 ches to this problem and illustrate these in examples.\nThis is joint work
  with Alla Detinko (Hull) and Dane Flannery (Galway).\n
LOCATION:https://researchseminars.org/talk/NYGroupTheory/3/
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