|DATE||August 05 (Thu), 2021|
|INSTITUTE||Research Institute for Mathematical Sciences, Kyoto University|
|TITLE||Geometric transitions for Calabi--Yau hypersurfaces|
Geometric transition is a process of connecting two smooth Calabi--Yau 3-folds by a birational contraction followed by a complex smoothing. It has attracted the interest of both mathematicians and physicists, since it may give the right notion to connect moduli spaces of Calabi--Yau 3-folds. For Calabi--Yau hypersurfaces in toric varieties, a well-known idea of constructing geometric transitions is the use of nested reflexive polytopes. However, the method fails if we are going in a naive way. In this talk, I will report the current situation of this approach by looking at the counterexample by Fredrickson and discuss how to save this idea.