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.