Caltech Logo

Logic Seminar

Thursday, May 31, 2018
3:00pm to 4:00pm
Add to Cal
Building 15, Room 131
Failure of the L^1 pointwise ergodic theorem for PSL_2(R)
Peter Burton, Department of Mathematics, University of Texas at Austin,

A 2015 example of Tao showed that the pointwise ergodic theorem for nonabelian free groups can fail for L^1 functions. This is in contrast to the situation for L^p, p >1.

We will present joint work with Lewis Bowen showing that this endpoint phenomenon also occurs for PSL_2(R). The proof involves analyzing the geodesic flow on an appropriately constructed hyperbolic surface.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].