SMS scnews item created by Zhou Zhang at Thu 9 Aug 2012 1512
Type: Seminar
Distribution: World
Expiry: 6 Sep 2012
Calendar1: 17 Aug 2012 1400-1500
CalLoc1: RC-4082 (UNSW)
Auth: zhangou@bari.maths.usyd.edu.au

# SYD-UNSW Joint Colloquium: Burns -- Algebraicization of Complex Manifolds 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: Friday, Aug. 17, 2--3PM

Room: RC-4082, Red Centre (UNSW)

Joint Colloquium web site:

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

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Title: Algebraicization of Complex Manifolds and the Complex
Monge-Ampère Equation

Abstract: Kodaira’s embedding theorem shows how to use
potential theory on a compact complex manifold X to
characterize when it admits a holomorphic embedding
into the complex projective space, i.e., is projective
algebraic. Cornalba and Griffiths, in the early ‘70’s,
began trying to use complex analytic growth techniques
to understand affine algebraic (in particular, non-compact)
manifolds. There are several ways to approach this,
using in various proportions complex differential
geometry and potential theory on such open manifolds.
The problem is to characterize the “slowest growing”
entire functions on X and showing, eventually, these
are the polynomial functions on an affine variety.
There are several approaches to this problem, no one
of which is, to this date, entirely satisfactory.
Several such approaches will be described, each
corresponding to a different characteristic picture
of a closed algebraic variety in affine space, and
various solutions of the homogeneous complex Monge-Ampère
equation used to measure intrinsically the growth of
X at infinity. This represents work partly joint with
Raul Aguilar and Zhou Zhang.

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Lunch with speaker: we meet around 12:30PM at the
entrance to the East Wing of Red Centre Building.

One choice of commuting from Sydney: meet at Carslaw
620 around 12:05PM and share taxi to UNSW. The round
trip is covered by department colloquium fund.


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