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)

Speakers

• Ekaterina Amerik (HSE, Moscou)

Automorphisms of hyperkähler manifolds via lattice embeddings

• Nicolas Bergeron (UPMC)

On O’Grady’s generalized Franchetta conjecture

• Fedor Bogomolov (NYU Courant Institute)

On invariant domains for automorphisms of infinite orderof projective varieties

• Yohan Brunebarbe (Ecole Polytechnique Fédérale de Lausanne)

A strong hyperbolicity property of locally symmetric varieties

• Frédéric Campana (Université de Lorraine)

Positive foliations and fibrations with (orbifold) rationally connected fibres

• Serge Cantat (Université de Rennes 1 & ENS Paris)

From birational transformations to regular automorphisms

• Mark de Cataldo (Stony Brook University)

Frobenius semisimplicity and surjectivity

• Fabrizio Catanese (University of Bayreuth)

New examples of rigid varieties and criteria for fibred surfaces to be
K (pi, 1)-spaces

• Jérémy Daniel (Ecole Normale Supérieure)

Variations of loop Hodge structures

• Alexandru Dimca (Université Nice Sophia Antipolis)

A computational approach to Milnor ber cohomology

• Richard Hain (Duke University)

Galois actions on unipotent fundamental groups of curves

• Vincent Koziarz (Université de Bordeaux)

Maximal representations of uniform complex hyperbolic
lattices

• Madhav Nori (University of Chicago)

CM Hodge structures

• Mihnea Popa (Northwestern University)

Hodge ideals

• Pierre Py (Université de Strasbourg)

Kähler groups and CAT(0) cubical complexes

• Xavier Roulleau (Université de Poitiers)

Construction of new simply connected surfaces of general type

• Stefan Schreieder (University of Bonn)

Algebraic structures with unbounded Chern numbers

• Carlos Simpson (Université Nice Sophia Antipolis)

Rank 3 rigid representations of projective fundamental groups

• Matthew Stover (Temple University)

Variations on an example of Hirzebruch

• Zhiyu Tian (Université Grenoble Alpes)

Fake Tori

• Bertrand Toen (Université de Toulouse)

Matrix factorizations and Bloch’s conductor formula