Special Day on Complex Geometry and PDE
Columbia UniversityThursday October 21, 2010
Department of Mathematics
All are invited to attend, there is no registration.
Schedule
12.15pm  1.05pm
Room Math 507 
Zbigniew Błocki (Jagiellonian University)
On the L^{∞}estimate in the CalabiYau theorem
 Abstract
We will present a simple pluripotential theoretic
proof of the uniform estimate for the complex MongeAmpère
equation on compact Kähler manifolds. One of its
advantages is that it allows one to use only the local version
of Kołodziej's L^{p}estimate in order to get the global
version. Secondly, the argument is easily adaptable to the case
of Hermitian manifolds, thus giving an alternative proof
of the uniform estimate recently obtained by Tosatti
and Weinkove.

1.05pm  2.30pm 
Lunch Break

2.30pm  3.20pm
Room Math 520 
Zhiqin Lu (UC Irvine)
A complex geometric proof of the TianYauZelditch expansion

3.20pm  4.00pm 
Coffee Break

4.00pm  4.50pm
Room Math 520 
Sławomir Kołodziej (Jagiellonian University)
Hölder continuity of solutions to the complex MongeAmpère equation

5.00pm  5.50pm
Room Math 520 
Steve Zelditch (Northwestern University)
The Cauchy problem for the homogeneous Monge Ampère equation
 Abstract
This is joint work with Yanir Rubinstein. We study the initial value problem
for the geodesic equation in the space of Kähler metrics in a fixed class. We frame
a general conjecture on the solution of the problem and verify it for toric Kähler
manifolds and Abelian varieties (with torus invariant metrics). It turns out that
except for special initial velocities, the solution only has a finite lifespan in this case.

Organizers: D.H. Phong, V. Tosatti