Jarod Alper

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

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.

Christina Delfs

Isogenies between Supersingular Elliptic Curves over Fp

Abstract: The problem of computing an isogeny between two given elliptic curves has been studied by many authors and
has several applications in computational number theory and cryptography. In the case of ordinary elliptic curves the
computation is based on the volcano-like structure of the isogeny graph, which provides a connection to ideal class groups.
The arising algorithm is sufficiently fast under the assumption of GRH. In the supersingular case though, the isogeny graph
is very irregular and this approach does not work. The currently fastest algorithm for finding isogenies between supersingular
curves performs a random walk on the fully-connected supersingular isogeny graph over Fp2 and is considerably slower
than the algorithm for ordinary curves.
In this talk we will restrict to isogenies between supersingular elliptic curves over the prime field Fp and examine the corresponding
subgraph of the supersingular isogeny graph. We will show some results about this graph that bear resemblance to the ordinary
case and help to adapt the algorithm to this situation. It turns out that we are able to construct isogenies between supersingular
curves over Fp as fast as in the ordinary case. Finally we shortly discuss the possibilities to use this algorithm to obtain an
improved algorithm for the computation of isogenies between arbitrary supersingular elliptic curves.
This is joint work with Steven Galbraith from University of Auckland in New Zealand.

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.

Lars Kindler

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

Fabian Müller

Title: The final log canonical model of M6

Abstract:  We describe the birational model of M6 given by quadric hyperplane sections of the degree 5 del Pezzo surface.
We explicitly analyze the birational map from M6 to this model and show that it is the last non-trivial space in the log minimal
model program for M6. As an application, we derive a new upper bound for the moving slope of the moduli space.

Sönke Rollenske

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).