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\begin{document}

\title[Complex, Contact, and Symplectic Geometry]{First International Joint Meeting AMS-UMI\qquad\qquad\qquad\qquad\qquad\qquad
Special Session\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad {\em Complex, Contact, and Symplectic Geometry}}
\maketitle
\section{program}

\begin{itemize}
\item 09.30-10.30 G. Tian: {\em Extremal Metrics and Geometric Stability}
\item 10.40-11.10 R. Paoletti: {\em Sz\"ego Kernels, Finite Group Actions, and the Volume of Big Line Bundles}
\item 11.10-11.40 coffee break
\item 11.40-12.40 Eugenio Calabi: {\em Function Spaces of Kaehler Metrics and Their Differential Geometries, Smooth or Otherwise}

\vspace{0.3cm}

\item 15.00-16.00 G. Matic: {\em Horizontal Contact Structures on Seifert fibered 3-manifolds}
\item 16.10-16.30 T. Pacini: {\em Deformations of Non-Compact Special Lagrangian Submanifolds}
\item 16.40-17.10 C. Arezzo: {\em Minimal Surfaces in Kahler-Einstein Manifolds of Positive Curvature}
\end{itemize}

\section{Abstracts}

\begin{enumerate}
\item G. Tian: {\em Extremal Metrics and Geometric Stability} 

\n This talk will discuss some results on existence of extremal metrics and 
its connection to geometric stability of underlying manifolds.

\vspace{0.2cm}

\item R. Paoletti: {\em Sz\"ego Kernels, Finite Group Actions, and the Volume of Big Line Bundles}

\n Almost complex quantization generalizes classical concepts and
constructions from algebraic geometry to almost complex symplectic manifolds. In turn, some of the analytic methods developped in this more general framework offer results not proved by previous techniques, or new approaches to established results. Here we shall study the behaviour of almost complex quantization
under finite group actions, and draw some consequences about the linear series associated to the irreducible representations of the group.

\vspace{0.2cm}

\item E. Calabi: {\em Function Spaces of Kaehler Metrics and Their Differential Geometries, Smooth or Otherwise}
\n We describe smooth or non smooth connections on the space of K\"ahler metrics over a compact manifold.

\vspace{0.2cm}

\item G. Matic: {\em Horizontal Contact Structures on Seifert fibered 3-manifolds}

\n We prove a complete criterion for a Seifert fibered
3-manifold to carry a contact structure transverse to a fiber. Notice
that it can be thought of as a contact version of the classical
Milnor-Wood inequality.

\item T. Pacini: {\em Deformations of Non-Compact Special Lagrangian Submanifolds}
\n In recent years, string theory and mirror symmetry have created 
new interest in Calabi-Yau manifolds and Special Lagrangian submanifolds.
In 1998, McLean studied the deformations of compact SL submanifolds. We 
present a similar result for the non-compact, "asymptotically flat", case.

\vspace{0.2cm}

\item C. Arezzo: {\em Minimal Surfaces in Kahler-Einstein Manifolds of Positive Curvature}

\n In this talk we present a general method to construct 
stable symplectic minimal submanifolds in K-E manifolds which are not 
holomorphic. By linking the existence of such objects to 
Ljusternick-Schnirelman theory and the deformation theory of
holomorphic submanifolds of a deforming algebraic manifold,
we prove for example the existence of stable symplectic 
non holomorphic minimal two spheres in algebraic surfaces of general
type, in $P^1\times P^2$\,, and of surfaces of higher genus in K-E 
hypersurfaces near Fano Fermat's manifold of sufficiently big dimension.

\end{enumerate}
\end{document}






