Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Torelli Theorem of $ALH^*$ Gravitational Instantons
Yu-Shen Lin (Boston University)
Abstract:
Gravitational instantons are non-compact complete hyper-Kahler 4-manifolds with
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%5E2%24&chf=bg,s,333333&chco=ffffff)
curvatures. They are introduced by Hawkings as the building blocks of his quantum gravity theory. The gravitational instantons are classified by their volume growths into types
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALE%24&chf=bg,s,333333&chco=ffffff)
,
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALF%24&chf=bg,s,333333&chco=ffffff)
,
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALG%24&chf=bg,s,333333&chco=ffffff)
,
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALH%24&chf=bg,s,333333&chco=ffffff)
, and
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALG%5E*%24&chf=bg,s,333333&chco=ffffff)
,
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALH%5E*%24&chf=bg,s,333333&chco=ffffff)
. In this talk, I will give a short proof of the Torelli theorem of gravitational instantons of type
![](https://chart.googleapis.com/chart?cht=tx&chl=%24ALH%5E*%24&chf=bg,s,333333&chco=ffffff)
, namely their corresponding hyper-Kahler triples are completely determined by the cohomology classes of their hyper-Kahler triple. The proof is inspired by the SYZ mirror symmetry of log Calabi-Yau surfaces. This is a joint work with T. Collins and A. Jacob.
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