**abstract:**
For a compact K"ahler manifold \(X\) endowed with
a Hermitian positive holomorphic positive line bundle \(L\),
The Bergman metric at level \(p\)
is defined as the rescaled induced Fubini-Study metric
for the Kodaira embedding of \(X\) into
the projective space associated to \(L^p\).
A theorem of Tian said that this Bergman metric will converge
to the original Käher form. We will explain some of its implications
on the zero of radom sections of \(L^p\). Then we will explain
a symplectic analogue of Tian's theorem
with optimal convergence speed.

Wed 28 May, 10:00 - 11:15, Sala Conferenze Centro De Giorgi

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