Takeo Ohsawa (Nagoya)
- Title:  L^2 method in complete Kaehler families
- Abstract: It is well known that a continuous function $f$ on a pseudoconvex domain $D$ in $mathbb{C}^n$ is holomorphic if and only if the complement of its graph ${(z,f(z)); zin$D$}$ in $Dtimesmathbb{C}$ is pseudoconvex (Hartogs 1909). It will be shown by an $L^2$ method that "pseudoconvex" can be weakened to "complete Kaehler". Nishino showed that any Stein family of $mathbb{C}$ over the disc is trivial. It will be shown by a similar $L^2$ method that the result still holds for complete Kaehler families. 

Marco Abate (Pisa)

- Title: Carleson measures and Toeplitz operators on weighted Bergman spaces

- Abstract: Carleson measures were introduced by Carleson in his celebrated solution of the corona problem; since then they have become an interesting subject of study on their own, mainly because they can be characterised in many different ways, both analytic and geometrical. In this talk we shall apply Carleson measures to the study of mapping properties of Toeplitz operators between weighted Bergman spaces on strongly pseudo convex domains. More precisely, if $T^beta_mu$ is the Toeplitz operator associated to the measure $mu$ and having as kernel the Bergman kernel of the weighted Bergman space $A^2_beta$, then (if $beta$ is large enough) $T^beta_mu$ maps $A^{p_1}_{alpha_1}$ into $A^{p_2}_{alpha_2}$ if and only if $mu$ is a Carleson measure of a suitable exponent. (Joint work with S. Mongodi and J. Raissy).

Dror Varolin (Stony Brook)

- Title: Holomorphic sections of vector bundles

- Abstract: I will present and sketch proofs of analogues of the celebrated direct image positivity theorems of Berndtsson.  The generalization involves looking at sections of holomorphic vector bundles of higher rank.  I will then use the results to establish L^2 extension theorems for sections of holomorphic vector bundles.   The main novelty is the proposal of a notion of Nakano-positive singular Hermitian metrics for holomorphic vector bundles, for which the L^2 extension theorem holds. 

Nessim Sibony (Orsay/KIAS)

- Title: Equidistribution in Nevanlinna's Theory.

- Abstract: The classical Nevanlinna theory is developed for maps from the complex plane with values in a projective variety.
Motivated by the theory of singular foliations by Riemann surfaces and their dynamics, I will study the case where the source space is hyperbolic. It could be the disc or the unit ball. I will give applications to foliations by Riemann Surfaces.

Sung Yeon Kim (KIAS)

- Title: Subelliptic multipliesr for dbar-Neumann problem

- Abstract: In 1979, J.J. Kohn proposed an algorithm to produce subelliptic multipliers for the dbar-Neumann problem. But Kohn’s original procedure gives no effective bound on the order of subellipticity in subelliptic estimates. In 2010, Y.-T. Siu obtained a new effective procedure to terminate Kohn’s algorithm for so-called special domains. In this talk, we explain Siu’s effective algorithm for multipliers as well as Kohn’s full radical algorithm and their difference. Then we present a triangular system of multipliers for special domains. We also propose a new class of geometric invariants, called jet vanishing orders, that permits us to obtain a new control of the effectiveness in the Kohn’s construction procedure of subelliptic multipliers for the special domains of finite D’Angelo type in C^3 . This is a joint work with D. Zaitsev.