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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Asymptotics of hyperboilic, Weil-Peterssen and Takhtajan-Zograf metrics

## Asymptotics of hyperboilic, Weil-Peterssen and Takhtajan-Zograf metricsAdd to your list(s) Download to your calendar using vCal - Melrose, R (Massachusetts Institute of Technology)
- Tuesday 28 July 2015, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Metric and Analytic Aspects of Moduli Spaces This will be a continuation of the talk by Xuwen Zhu on our joint work concerning the regularity of the fibre hyperbolic metrics up to the singular fibres for Lefschetz fibrations. In particular this applies to the universal curve over moduli space. I will discuss the marked case with the moduli space $mathcal{M}_{g,n}$ of surfaces of genus $g$ with $n$ ordered distinct points in the stable range, $2g+nge3.$ As in the unmarked case the description of the regularity of the fibre hyperbolic metrics, up to the divisors forming the `boundary’ of the Knudsen-Deligne-Mumford compactification, implies boundary regularity for the Weil-Peterssen metric. In this case it also leads to an asymptotic description of the Takhtajan-Zograf metric which contributes to the Chern form of the determinant bundle for $arpa$ on the fibres of the universal curve. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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