Moduli Spaces in Geometry 
October 26 – 30, 2015
Classification problems in Complex Geometry   often lead to  so-called moduli spaces. These are complex analytic spaces, algebraic varieties, or stacks whose points parameterize the isomorphy classes of the objects in question. Famous examples include the moduli space of smooth curves of fixed genus and moduli spaces of stable vector bundles on a fixed variety.

A well-known   construction method for such moduli spaces comes from GIT. This technique works   for vector and principal bundles with or without extra structures on projective algebraic varieties. The notion of  stability from GIT has to be translated into an intrinsic notion of  stability for the objects one would like to study. One of the striking and interesting discoveries, known under the name of Kobayashi-Hitchin correspondence, is the fact that moduli problems for stable objects are often related to  gauge theoretical moduli problems.  

It is a remarkable fact that the moduli stack of Higgs bundles features prominently in many aspects of the Langlands program.  Ngô Bào Châu used the topology of the moduli stack of Higgs bundles and the  Hitchin map to prove the fundamental lemma in the Langlands program over function fields over finite fields.  Drinfeld and Laumon proposed a geometric version of the Langlands program which works over arbitrary fields, in particular, over C. It postulates an equivalence between the derived category of D-modules on the moduli stack of principal G-bundles and the derived category of O-modules on the stack of local systems for the Langlands dual group on an algebraic curve. Donagi and Pantev showed that the Hitchin integrable system for a simple algebraic group   is dual to the Hitchin system for the Langlands dual group. This can be interpreted as a « classical limit » of the Geometric Langlands Conjecture. The workshop will discuss recent results related to these spectacular developments.

Scientific Committee

Nigel Hitchin (University of Oxford)
Eduard Looijenga (University of Utrecht)
Carlos Simpson (Université Nice Sophia-Antipolis)

Organizing Committee

Joseph Ayoub (University of Zurich)
Alexander Schmitt (Freie University Berlin)
Andrei Teleman (Aix-Marseille Université)


Cayley-Chow forms of K3 surfaces and Ulrich bundles

Non-perturbative symplectic manifolds and non-commutative algebras

Curve counting on Abelian surfaces and threefolds and Jacobi forms

Wall-crossing in quasimap theory

The uniformization of the moduli space of abelian 6-folds

Higgs sheaves on singular spaces and uniformisation for varieties of general

Motives connected with classical modular forms

Toric non-abelian Hodge theory

Some results on the cohomology of moduli spaces of Higgs bundles

Monopoles on Sasakian 3-folds

Torsion free sheaves with zero dimensional singularities

Kahler metrics on categories

An Andre-Oort conjecture for variations of Hodge structures

Geometry and moduli spaces of Gushel-Mukai varieties

Bogomolov’s inequality and its applications

Birational geometry of moduli spaces of K3 surfaces II

On the remodeling conjecture for toric Calabi-Yau 3-orbifolds

Unramied local L-factor and singularities in reductive monoid

Birational geometry of moduli spaces of K3 surfaces I

Segre classes and Hilbert scheme of points

On the proof of S-duality modularity conjecture on quintic threefolds

Moduli spaces for slope-semistable sheaves on projective manifolds