Room P3.10, Mathematics Building

William Kirwin, MPI, Leipzig
Adapted Complex Structures and the Geodesic Flow

I will present a new construction of adapted complex structures. Adapted complex structures provide one way to understand the "complexification" of a compact, real-analytic Riemannian manifold $M$. I will explain how a tubular neighborhood of $M$ in its tangent bundle inherits a "canonical" complex structure, the so-called adapted complex structure, and furthermore that this complex structure can be constructed using the "imaginary time" geodesic flow. Time permitting, I will also discuss some applications. (joint w/ Brian Hall)