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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, June  6, 2023}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Misha Verbitsky 
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  (IMPA)
}
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will talk about
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{\Large\bfseries Teichmuller spaces for geometric structures and the mapping class group action\par}
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\textsc{Abstract:}
The Teichmuller space of geometric structures of a given  type is a quotient of the (generally,
 infinite-dimensional) space of geometric structures by  the group of isotopies, that is, by the connected  component of the diffeomorphism group. In several  important qand smooth.uestions, such as for symplectic, hyperkahler,  Calabi-Yau, G2 structures, this quotient is  finite-dimenisional and even smooth. The mapping class  group acts on the Teichmuller space by natural  diffeomorphisms, and this action is in many important  situations ergodic (in particular, it has dense orbits),  bringing strong consequences for the geometry. I would  describe the Teichmuller space for the best understood  cases, such as symplectic and hyperkahler manifolds, and  give a few geometric applications.








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