**Michael Wiemeler, Mathematics Institute, Münster**

**Title:** Positive Curvature, Symmetries, and Matroids

**Abstract:** A 1930s conjecture of Hopf states that the Euler
characteristic of a positively curved even-dimensional manifold is
positive. In joint work with Lee Kennard and Burkhard Wilking we
showed this conjecture for simply connected manifolds M with
isometric, effective T^{5}-action. If there is an isometric,
effective T^{7}-action on M and the odd-degree rational cohomology
of M vanishes, we can also compute the rational cohomology ring of
M.
In this talk I will discuss a similar result where the above
cohomological condition is replaced by a "more geometric" one. Its
proof is an application of matroid theory. The results presented in
this talk are joint work with Lee Kennard and Burkhard Wilking.