Abstracts for MPI-Oberseminar

I will start by recalling some basic facts on the first eigenvalue of
the Laplacian on a compact Riemannian manifold. Next I will discuss a
classical theorem of Hersch, which says that on the 2-sphere the first
eigenvalue is the largest possible when the metric is the standard
one.

I will then formulate the analogous problem for Kaehler metrics and
will describe the solution in the case of Hermitian symmetric
spaces of the compact type. If time permits I will try to explain the
link with Satake-Furstenberg compactifications and coadjoint orbits.

An orbitope is the convex hull of an orbit of a compact Lie group acting linearly on a vector space. In this talk we will discuss the convex hull of a coadjoint orbit (i.e. a coadjoint orbitope) and we will describe how  the face structure of this convex body can be studied by means of the momentum map.  We will also explain the link between Satake-Furstenberg compactifications and coadjoint orbitopes, which is one of  the motivations to study these convex bodies.

MPI-Oberseminar/Worshop Galois represenations and pencils of Calabi-Yau motives

In this talk, a Laurent polynomial f is mirror-dual to a Fano manifold X if the Picard-Fuchs operator
of f equals the quantum differential operator of X. I introduce the class of Minkowski polynomials
and show how to use them to derive the classification of Fano 3-folds (Iskovskikh, Mori--Mukai)
from. I outline a program to classify Fano 4-folds using these ideas. At the end I briefly touch
on extremal and low ramification sheaves.