Abstracts for MPI-Oberseminar

Enumerative geometry is a branch of classical algebraic geometry whose
aim is to count the solutions to a given problem. As an example, given
four general lines in 3-space, there are exactly two other lines
meeting each of them simultaneously. The solution to such a problem is
usually found by constructing a "moduli space" (in the example the
Grassmann 4-manifold G of lines in 3-space) and then doing
"intersection theory" on it (computing the number of points, or
degree, of the intersection of M(L_I). I=1,...4, where M(L) is the cod

The little $n$-cubes operads have been introduced to encode operations
acting on $n$-fold loop spaces. Operads homotopy equivalent to little
$n$-cubes (called $E_n$-operads) are also used in algebra, in order to  model a
full scale of homotopy commutative structures, from fully  homotopy
associative but non-commutative ($n=1$) until fully homotopy  associative and
commutative ($n=\infty$).

The main objective of this talk is to explain that the
Grothendieck-Teichmüller group, as defined by Drinfeld in the rational

A key concept in Riemannian geometry is special holonomy. A particular instance of
this is provided by G2-manifolds which are 7-dimensional and carry a 3-form of
special algebraic type. This fundamental form induces a metric and is parallel with
respect to the associated Levi-Civita connection. We will interpret this is as an
Euler-Lagrange equation of a certain energy functional and show that the moduli
space of parallel forms is smooth. The talk is based on joint work with Hartmut Weiss.
 

Motivated by noncommutative quantum field theory, we construct a  non-formal deformation
quantization of the Heisenberg supergroup. This  deformed star-product provides a universal
deformation formula, namely  it deforms algebras on which the Heisenberg supergroup is acting.
In  this context, we are led to consider the notions of Hilbert superspace  and C*-superalgebra,
compatible with the deformation.