A question of Gromov asks:
Is it true that every compact manifold is a quotient of a hyperbolic space by a discrete group of isometries?
I will explain how one can use this question to prove that the fundamental groups of compact symplectic Calabi-Yau six-manifolds can be arbitrary.
The talk is based on the joint work with Anton Petrunin and Joel Fine:
arXiv:1108.5964: The diversity of symplectic Calabi-Yau six-manifolds
arXiv:1104.4814: Telescopic actions
arXiv:0802.3648: Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold
The time and the place: Fri, Nov 18, 2011, 16:00-18:00; IPMU Balcony A