ICTP Maths Seminar NEXT WEEK

[Math]

MATHEMATICS SEMINARS 2007


Tuesday, 27 March, at 14.00 hrs.



Dr. Valentino Tosatti

(Harvard University)



"The Calabi-Yau equation on symplectic manifolds"



Abstract:

Abstract: We consider the problem of prescribing
the volume form of a symplectic form compatible
with a given almost-complex structure on a
compact symplectic manifold. When the complex
structure is integrable, and the manifold is
therefore Kaehler, this is the celebrated
Calabi conjecture that was solved by Yau
30 years ago. Donaldson has recently conjectured
that in dimension 4 the equation is still
solvable, and has shown that this would have
striking consequences in symplectic topology.
In a joint work with Ben Weinkove and Shing-Tung
Yau we show that the necessary a priori estimates
can be reduced to an integral estimate of a scalar
function, and that the conjecture holds under
a positive curvature condition.


Venue:  ICTP Seminar Room, Main Building, first floor