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SUMMARY:Marco Boggi (UFMG Belo Horizonte)
DTSTART:20200506T120000Z
DTEND:20200506T130000Z
DTSTAMP:20260423T010943Z
UID:AGSeminar/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGSeminar/6/
 ">Automorphisms of procongruence mapping class groups</a>\nby Marco Boggi 
 (UFMG Belo Horizonte) as part of Sapienza A&G Seminar\n\n\nAbstract\nIn th
 is talk\, I will discuss the automorphism group of the procongruence mappi
 ng class group and of the associated procongruence curve and pants complex
 es. In analogy with a classical result of Ivanov for mapping class groups\
 , this allows to determine the group of automorphisms of the $arithmetic$ 
 procongruence mapping class group which satisfy a natural geometric condit
 ion. It is a nontrivial fact that this condition holds in genus $0$. Let $
 \\mathcal{M}_{0\,n}$ be the moduli space of $n$-labeled\, genus $0$ algebr
 aic curves. It follows\, in particular\, that $\\mathrm{Out}(\\pi_1^\\math
 rm{et}(\\mathcal{M}_{0\,n}\\otimes\\Q))\\cong\\Sigma_n$ for $n\\geq 5.\\ne
 wline$\nThis talk is based on a joint work with Louis Funar and Pierre Loc
 hak  (cf. $\\texttt{arXiv:2004.04135}$).\n
LOCATION:https://researchseminars.org/talk/AGSeminar/6/
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