EVENT DETAILS AND ABSTRACT

Title: Magnetic complex structures on cotangent bundles
Speaker: Brian Hall
Speaker Info: University of Notre Dame
Brief Description:
Special Note:
Abstract:

I will describe joint work with Will Kirwin on using "imaginary time flows" to construct complex structures on cotangent bundles. First, I will discuss the geodesic flow. If one starts with the vertical polarization on a cotangent bundle and pushes forward by the "imaginary time geodesic flow", the result is a complex polarization, which turns out to be the adapted complex structure of Lempert-Szőke and Guillemin-Stenzel. If one instead uses a magnetic flow—describing the motion of a charged particle in the presence of a magnetic field—the resulting complex structure is new. I will describe several different ways of interpreting the imaginary-time flow and will discuss two concrete examples.