SMS scnews item created by Zhou Zhang at Thu 9 Aug 2012 1458
Type: Seminar
Distribution: World
Expiry: 6 Sep 2012
Calendar1: 14 Aug 2012 1200-1300
CalLoc1: AGR Carslaw 829
Auth: zhangou@bari.maths.usyd.edu.au

# GTA Seminar: Burns -- Holomorphic Extension and the Complex Monge-Ampère Equation

Speaker: Prof. Daniel Burns (University of Michigan, Ann Arbor)

http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=dburns

Time: Tuesday, August 14, 12(NOON)--1PM

Room: AGR (Carslaw 829)

Lunch: after the talk (at Taste at Sydney Uni, i.e.
"Law School Annex Cafe")

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Title: Holomorphic Extension and the Complex Monge-Ampère
Equation

Abstract: some time ago, Boutet de Monvel proved a Paley-Wiener
type theorem for compact real analytic manifolds M, relating
the exponential rate of convergence of the eigenfunction
expansion of a real analytic function f with respect to an
elliptic operator P with the radius of holomorphic extension
of said function into the complex domain, i.e., into a
neighborhood of M in its complexification. We discuss what
happens when one wants to study this extension globally.
This leads to holomorphic differential geometric properties
of global complexifications, and especially exhaustions by
solutions of the homogeneous complex Monge-Ampère equation.
We also discuss another approach to these questions using
the Toeplitz operators of Boutet de Monvel and Guillemin.
This is joint work with Zhou Zhang and with Victor Guillemin.

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Web site for Geometry Seminar is at:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html


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