Title:Associated forms in classical invariant theoryAbstract: There is an interesting map which associates to a homogeneous form on Cof degree d with non-vanishing^{n}

discriminant, a form on Cof degree n(d-2). It was conjectured in a recent paper by M. Eastword and A. Isaev that all^{n}

absolute classical invariants of forms on Cof degree d can be extracted from those of forms of degree n(d-2) via this^{n}

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 BöhningTitle:On the Hodge-theoretic approach to the irrationality problem for cubic fourfoldsAbstract: 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.

Title:

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 F

than the algorithm for ordinary curves.

In this talk we will restrict to isogenies between supersingular elliptic curves over the prime field F

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 F

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 EbelingTitle:Gabrielov numbers of cusp singularities with group actionAbstract: 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 characteristicAbstract: 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

D-modules.

Title:

Abstract: We describe the birational model of M

We explicitly analyze the birational map from M

model program for M

Sönke Rollenske

Title:Classification of stable surfaces: first stepsIn 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 (K_{X})=1^{2}

(work in progress with Marco Franciosi and Rita Pardini).