Online Talk 

Zoom link: https://princeton.zoom.us/j/92116764865

Passcode: 114700

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.