May 30-June 3, 2016
This workshop will present recent advances concerning the topology of complex algebraic varieties. This topic, which originated in the works of Zariski and Lefschetz, has seen many developments in the past few years, in various directions. The following themes will be considered:
– the structure of the fundamental groups of smooth complex projective varieties. While Serre’s question of characterizing such groups among finitely presented groups remains completely open, many restrictions have been obtained, in particular concerning their finite dimensional representations.
– the Shafarevich conjecture, which predicts that the universal cover of a smooth complex projective variety is holomorphically convex.
– Hodge theory, in particular the recent use of Saito’s mixed Hodge modules towards topological results.
– the relations between hyperbolic geometry and algebraic varieties (study of the Cremona group, action of Kahler groups on trees…).
The workshop will try to develop interactions between experts on topics as diverse as hyperbolic geometry, geometric group theory, D-modules or non-abelian Hodge theory around central problems of complex algebraic geometry.
Scientific & Organizing Committee
Philippe Eyssidieux (Université Grenoble Alpes)
Bruno Klinger (UPMC-Paris Diderot)
Dieter Kotschick (University of Munich)
Domingo Toledo (University of Utah)
Automorphisms of hyperkähler manifolds via lattice embeddings
On O’Grady’s generalized Franchetta conjecture
On invariant domains for automorphisms of infinite orderof projective varieties
A strong hyperbolicity property of locally symmetric varieties
Positive foliations and fibrations with (orbifold) rationally connected fibres
From birational transformations to regular automorphisms
Frobenius semisimplicity and surjectivity
New examples of rigid varieties and criteria for fibred surfaces to be
Variations of loop Hodge structures
A computational approach to Milnor ber cohomology
Galois actions on unipotent fundamental groups of curves
Maximal representations of uniform complex hyperbolic
CM Hodge structures
Kähler groups and CAT(0) cubical complexes
Construction of new simply connected surfaces of general type
Algebraic structures with unbounded Chern numbers
Rank 3 rigid representations of projective fundamental groups
Variations on an example of Hirzebruch
Matrix factorizations and Bloch’s conductor formula