Title: Associated forms in classical invariant theory Abstract: There is an interesting map which associates to a homogeneous form on Cn of degree d with non-vanishing
discriminant, a form on Cn of degree n(d-2). It was conjectured in a recent paper by M. Eastword and A. Isaev that all
absolute classical invariants of forms on Cn of degree d can be extracted from those of forms of degree n(d-2) via this
map. This surprising conjecture was motivated by the well-known Mather-Yau theorem for isolated hypersurface
singularities. I will report on joint work with A. Isaev which settles this conjecture in full generality and proves a stronger statement in the case of binary forms.
Christian Böhning Title: On the Hodge-theoretic approach to the irrationality problem for cubic fourfolds Abstract: We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface
is decomposable. This disproves a conjecture of Kulikov related to a Hodge theoretic approach to proving the irrationality
of the very general cubic fourfold. We also discuss some possibilities to modify this approach, and, if time permits, some
alternative approaches (categories, dynamical spectra).
This is joint work with Asher Auel and Hans-Christian von Bothmer.
Wolfgang Ebeling Title: Gabrielov numbers of cusp singularities with group action Abstract: Gabrielov numbers describe certain Coxeter-Dynkin diagrams of the 14 exceptional unimodal singularities and
play a role in Arnold's strange duality. The Berglund-Hübsch-Henningson duality gives a mirror symmetry between orbifold
curves and cusp singularities with group action generalizing Arnold's strange duality. We define Gabrielov numbers for a
cusp singularity with an action of a finite group of diagonal symmetries. Using the McKay correspondence, we study the
topology of a crepant resolution of the quotient of complex 3-space by such a group and the preimage of the Milnor fibre
of the cusp singularity. We construct a Coxeter-Dynkin diagram where one can read off the Gabrielov numbers.
This is joint work with Atsushi Takahashi.
Title: Local-to-global extensions of D-modules in positive characteristic Abstract: I will present several generalizations of results from Katz' seminal article "Local-to-global extensions of
representations of fundamental groups" (Ann. Inst. Fourier (Grenoble) 36 (1986), no. 4) to the context of O-coherent
Title: Classification of stable surfaces: first steps In analogy to the case of curves, the Gieseker moduli space of surfaces of general type admits a natural compactification,
the moduli space of stable surfaces. A basic question is "What techniques and results on surfaces of general type carry
over to this larger class of surfaces?" I will first present some general results on pluricanonical maps and geography of stable surfaces (joint with Wenfei Liu).
These will be complemented with partial results in the test case of Gorenstein stable surfaces with (KX)2=1
(work in progress with Marco Franciosi and Rita Pardini).