# Meeting Details

Title: Interactions of topology and measure rigidity Department of Mathematics Colloquium Federico Rodriguez Hertz In the last several years a strong interaction between topology and measure rigidity for some higher rank actions has been discovered. However, for quite some time the experts believed that in this interaction it was topology that influenced the measurable structure of the action. Recently it has been understood that the interaction is indeed a two-way traffic: it works in the opposite direction as well, the measurable structure of the action imposes some strong requirements on the topology of the space. For example, such a soft requirement as the presence of an invariant measure with nonzero Lyapunov exponents implies very strong restrictions on the topology of the manifold, thus opening the door to the solution of some old conjectures on the classification of higher rank actions, e.g., the classification of positive entropy, measure preserving actions of $SL(n,\Z)$ on $n$-dimensional manifolds. In this talk I will describe this new direction of research that combines topology, measure theory and higher rank actions of Lie group. The talk will be accessible to non-experts and graduate students.