CMSA Math Science Literature Lecture Series


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November 25, 2020 9:00 am - 10:30 am

Eduard Jacob Neven Looijenga - Tsinghua University & Utrecht University

TITLE: Theorems of Torelli type

ABSTRACT: Given a closed manifold of even dimension 2n, then Hodge
showed around 1950 that a kählerian complex structure on
that manifold determines a decomposition of its complex
cohomology. This decomposition, which can potentially vary
continuously with the complex structure, extracts from a non-linear
given, linear data. It can contain a lot of information. When there
is essentially no loss of data in this process, we say that the Torelli
theorem holds. We review the underlying theory and then survey
some cases where this is the case. This will include the classical
case n=1, but the emphasis will be on K3 manifolds (n=2) and
more generally, on hyperkählerian manifolds. These cases stand
out, since one can then also tell which decompositions occur.

Talk chair: Shing-Tung Yau

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

For more information, please visit the event page.

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