Schedule:

Location:

Abstracts:

Reynir Axelsson

Title: Kähler structure on Hurwitz spaces.

Abstract: A generalized Weil-Petersson metric is introduced together with a determinant line bundle and a Quillen metric/Deligne pairing.

Daniel Barlet

Title: Two semi-continuity results for the algebraic dimension of compact complex manifolds.

Abstract: Using some relative codimension 1 cycle-space method, we give, following the ideas of D. Popovici, semi-continuity results for the algebraic dimension in a family a compact complex manifolds parametrized by a disc.

Indranil Biswas

Title: Approximate Yang-Mills-Higgs metrics

Abstract:  Let E_G be a principal G-bundle over a compact connected Kähler manifold, where G is a connected reductive linear algebraic group defined over C. We show that E_G is semistable if and only if it admits approximate Hermitian-Einstein structures. A similar result is also proved for flat Higgs bundles over affine manifolds. (Joint work with Steven Bradlow, Adam Jacob, John Loftin and Matthias Stemmler.)

Nicholas Buchdahl

Title: The Weil-Petersson metric on moduli spaces of stable bundles

Abstract: Moduli spaces of one kind or another are well-known to carry interesting geometric structures, often induced by some kind of tautological construction. A standard example is the Weil-Petersson metric on Teichmüller spaces of marked Riemann surfaces. Another good example is that of the L^2 metric on moduli spaces of stable holomorphic vector bundles over a compact Kaehler manifold, also known as as ``Weil-Petersson metric".
In this case, it is of particular interest to understand how this metric degenerates towards the ``boundary" of the moduli space.

In this talk, I will report on joint work (still in progress) with Georg Schumacher, in which we are attempting to get a better understanding of this metric and its degenerations, particularly in the case of stable holomorphic bundles over compact Kähler surfaces.

Jean-Pierre Demailly

Title: Towards the Green-Griffiths-Lang conjecture

Abstract: The talk will investigate the Green-Griffiths-Lang conjecture, stating that all entire curves drawn in projective varieties of general type are contained in a proper algebraic subvariety. We will explain a few techniques ideas involving holomorphic Morse inequalities for jet bundles, and some new variations in their application to the conjecture.

Gerd Dethloff

Title: Value distribution of the Gauss map of complete minimal surfaces

Abstract: In this talk we study the ramification of the Gauss map of complete minimal surfaces in R^n on annular ends. Our results improve results by Jin-Ru (in the general case) and more special ones by Kao (in the case of R^3), always in the sense that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. The main proof idea is to construct and to compare explicit singular flat and negatively curved complete metrics with ramification on these annular ends and then to adapt technics similar to those used by Fujimoto, Jin-Ru and Kao to finish the proofs.

Jun-Muk Hwang

Title: Deformation of the space of lines on the 5-dimensional hyperquadric

Abstract:  A nontrivial (global) deformation of the space of lines on the 5-dimensional hyperquadrichas been discovered by Pasquier-Perrin. We show that this is the only possible deformation.

Ngaiming Mok

Title:Rigidity phenomena for sub-VMRT structures on uniruled projective manifolds

Abstract:  Hong-Mok considered pairs (X₀;X) of uniruled projective manifolds, and established a non-equidimensional Cartan-Fubini Extension Principle (2010) in terms of a certain nondegeneracy condition on the second fundamental form for a pair (B ⊂ A) consisting of a VMRT A and a linear section B of A. The latter has led to the characterization of standard embeddings by Hong-Mok and Hong-Park (2011). Recently with Y. Zhang (2014) we have established a stronger rigidity phenomenon for sub-VMRT structures, where in place of a germ of mapping (X₀;0) ➞ (X;0) we consider a germ of submanifold (S;0) ⊂ (X;0) for a uniruled projective manifold X. Defining a sub-VMRT structure by taking intersections C_x(X) ∩ PT _x(S) we obtain sufficient conditions for S to extend to a rationally saturated projective subvariety Z ⊂ X.

Takeo Ohsawa

Title: A remark on Hörmander's isomorphism

Abstract: Hörmander's isomorphism theorem between two L^2 cohomology groups implies an extension theorem. This does not seem to
be included in the known injectivity theorems by Enoki, Kollár, Fujino and others.

Thomas Peternell

Title: On the minimal model program for Kähler threefolds

Abstract: I will describe recent progress in joint work with Andreas Höring on the minimal model program for 3-dimensional Kähler
varieties, with special regard to abundance.

Yum-Tong Siu

Title: Strong rigidity and Hodge filtration in homology setting

Abstract: For a compact Kähler manifold the Hodge filtration filters cohomology classes by representability by closed forms of type (p; q). In this talk we use the method of strong rigidity to discuss Hodge filtration in the homology setting by considering the representability of homology classes by CR manifolds.