|Presentation Name：||Diffeomorphic classes of the doubling Calabi-Yau threefolds|
|Presenter：||Dr. Naoto Yotsutani|
It is well-known that there is only one compact Kahler manifold with zero first Chern class up to diffeomorphism in complex dimension 1 which is topologically a torus. This is an example of Calabi-Yau manifold and the Ricci-flat metric on a torus is actually a flat metric.
In dimension 2, the K3 surfaces furnish the compact simply-connected Calabi-Yau manifolds.
However in 3 dimension, it is an open problem whether or not the number of topologically distinct types of Calabi-Yau 3-folds is bounded.
From the view point of physics (String theory), S.T. Yau speculates that there is a finite number of families of Calabi-Yau 3-folds.
From the view point of mathematics, in turn, it has been conjectured by M. Reid that the number of topological types (or differential structures) of Calabi-Yau 3-folds is infinite.
In this talk, we consider how to distinguish two Calabi-Yau 3-folds by diffeo types building upon our previous work with M. Doi (NYJM. 20 (2014) 1-33).
|Annual Speech Directory：||No.5|
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