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Seminários do IMPA

Variedades de Calabi–Yau

Differential rings for non-compact Calabi-Yau varieties
Martin Vogrin

University of Hamburg
Terça-feira, 13 de agosto de 2019, 15:30
Sala 224

One of the main outcomes of the program Gauss-Manin Connection in Disguise is that finitely generated differential rings can be associated to Calabi-Yau varieties. The elements of the differential rings are generalizations of the classical modular forms and reduce to them in special cases. 

In my talk I will present some recent results on extending the program to a non-compact setting. After a short introduction to the compact case I will define differential rings for non-compact Calabi-Yau varieties from variation of mixed Hodge structure and comment on the implications of non-compactness on the structure of the Gauss-Manin (AMSY) Lie algebra. If time permits I will talk about the non-holomorphic completion of these rings coming from $tt^*$-geometry.