Abstracts

Manuel Amann, Westfälische Wilhelms-Universität Münster
Formality of positive quaternion Kähler manifolds
Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, such a manifold is a symmetric space. Recently, Positive Quaternion Kähler Geometry has become a rather popular field of study featuring a variety of different methods. After reviewing some known properties I shall offer a new approach via Rational Homotopy Theory which will reveal yet another analogy between Positive Quaternion Kähler Manifolds and symmetric spaces. pdf file


Owen Dearricott, University of California, Riverside
Positive curvature on a 3-Sasakian 7-manifold
We discuss a construction of a positively curved metric on a 3-Sasakian manifold obtained as a connection metric over a conformal self-dual Einstein orbifold. The method amounts to using a trick of Thorpe to test the positivity of the sectional curvature of a related curvature operator.


Nina Lebedeva, Westfälische Wilhelms-Universität Münster
Alexandrov spaces with maximal number of extremal points
We prove that Alexandrov n-space of nonnegative cuvature with 2ⁿ one-point extremal sets is a factor of Euclidean space by a discrete group of isometries.


Anton Petrunin, Westfälische Wilhelms-Universität Münster
Alexandrov meets Lott--Villani--Sturm
The talk is very technical. I will show compatibility of two definitions of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott--Villani--Sturm.


Catherine Searle, University of Cuernavaca, Mexico
Non-negatively curved manifolds with maximal symmetry rank in low dimensions
Abstract


Miles Simon, Universität Freiburg
Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
We consider complete (possibly non-compact) three dimensional Riemannian manifolds (M,g) such that:
a) (M,g) is non-collapsed (i.e. the volume of an arbitrary ball of radius one is bounded from below by v>0 ),
b) the Ricci curvature of (M,g) is bounded from below by k,
c) the curvature growth of (M,g) is not too extreme (or (M,g) is compact).
Given such initial data (M,g) we show that a Ricci flow exists for a short time interval [0,T), where T =T(v,k)>0. This enables us to construct a Ricci flow of any (possibly singular) metric space (X,d) which arises as a Gromov-Hausdorff limit of a sequence of 3-manifolds which satisfy a), b) and c) uniformly. As a corollary we show that such an X must be a manifold. This shows that the conjecture of M.Anderson-J.Cheeger-T.Colding-G.Tian is correct in dimension three.


Fred Wilhelm, University of California, Riverside
Principles for deforming nonnegative curvature
I will discuss some abstract principles for deforming nonnegative curvature and broadly out line the role these played in deforming the metric on the Gromoll-Meyer sphere to positive curvature. This is joint work with Peter Petersen. Slides