Special Day on Complex Geometry and Analysis on real analytic Riemannian manifolds

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

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.
Date: Saturday, February 21, 2015
Time: 04:30pm
Where: Swift 107
Contact Person: Valentino Tosatti
Contact email: tosatti@math.northwestern.edu
Contact Phone:
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