Speaker: Sergey Galkin

Title: Calabi-Yau threefolds: Age of Discovery?

Date: May 15, 2014, 18:00 - 20:20

Place: Iskovskikh seminar, Steklov 540

Abstract:

I'll give a brief overview of the so far discovered borders in the geography of Calabi-Yau threefolds.
Mostly I'll be concerned with two (conjecturally almost symmetric) borders:
Calabi-Yau threefolds with Picard number one (and also with the related question of Fano fourfolds with Picard number one),
and Calabi-Yau threefolds with one-dimensional moduli space (also rigid Calabi-Yau threefolds, that violate mirror symmetry).
I know about a hundred examples, including some hypothetical, and about fifty examples that I am confident in.
There are less than ten various constructions, that I’ll try to review.
Time permits, I’ll tell some new constructions that produce about a dozen new examples (or realize some of the old hypotheses).