This is a workshop on the connections between topological invariants of possibly non-complete normal complex varieties and other invariants, especially those coming from birational geometry and affine algebraic geometry. One focus will be on results and techniques that have deepened our understanding of the fundamental group in connection with the Shafarevich Problem on the holomorphic convexity of the universal cover of a smooth projective varieties, an area which has seen quite a lot of major recent advances. Another focus will be on advances in (affine) algebraic geometry coming from studying the interaction of algebraic and topological properties of open varieties. Of particular interest in the case of surfaces is the study of the topology of their singularities with its connections to 3-manifolds. Another interest is the key role played by the Bogomolov-Miyaoka-Yau inequality for open normal surfaces relating the (logarithmic) Chern numbers of these surfaces and local data coming from the singular points.

A series of Aisenstadt Chair lectures will be delivered by Fedor Bogomolov (Courant Institute, NYU).

The workshop will be preceded by three mini-courses running from September 21 to September 23:

  • 1. Topological methods in the study of singularities (Anne Pichon and Walter Neumann).
  • 2. The Shaferevich Conjecture and the Fundamental Group (Terence Napier and Mohan Ramachandran).
  • 3. Logarithmic genera and the BMY-inequality (Ryoichi Kobayashi, Adrian Langer).