Tuesday, Oct 15

Wednesday, Oct 16






09h1510h15

Mihai 
14h00  15h00

VietAnh

* 
coffee



coffee

10h3011h30

Renato

15h2016h20

Cezar 


lunch

16h30  17h30

Piotr





*

dinner





ViêtAnh Nguyên Holomorphic sections of line bundles vanishing along subvarieties
Abstract. Let $X$ be a compact normal complex space of dimension n, and $L$ be a holomorphic line bundle on $X$. Suppose $\Sigma=(\Sigma_1,\ldots,\Sigma_l)$ is an $l$tuple of distinct irreducible proper analytic subsets of $X$, $\tau=(\tau_1,\ldots,\tau_l)$ is an $l$tuple of positive real numbers, and consider the space $H^0_0 (X, L^p)$ of global holomorphic sections of $L^p:=L^{\otimes p}$ that vanish to order at least $\tau_{j}p$ along $\Sigma_{j}$, $1\leq j\leq\ell$. We find necessary and sufficient conditions which ensure that $\dim H^0_0(X,L^p)\sim p^n$, analogous to JiShiffman's criterion for big line bundles. We give estimates of the partial Bergman kernel, investigate the convergence of the FubiniStudy currents and their potentials, and the equilibrium distribution of normalized currents of integration along zero divisors of random holomorphic sections in $H^0_0 (X, L^p)$ as $p$ tends to infinity. Regularity results for the equilibrium envelope are also included. This is a recent jointwork with Dan Coman (Syracuse University) and George Marinescu (Universität zu Köln).
Cezar Joita The image problem for analytic map germs
Abstract. The image of an analytic
map germ $(X, x)\to (Y, y)$ may or may not be open.
We provide the proof of a criterion which has been conjectured in 1971 by Huckleberry.
More generally, the image of an analytic map germ may or may not be welldefined as a set germ at $y$.
We find classifying conditions for holomorphic map germs $(\mathbb C^{n}, 0) \to (\mathbb C^{2}, 0)$,
and for a special class of real analytic map germs $(\mathbb R^{2n}, 0) \to (\mathbb R^{2}, 0)$.
(jointwork with Mihai Tibar).
Piotr Migus The Łojasiewicz
inequalities  some open problems
Abstract.
We recall different types of the Łojasiewicz inequality and known
results in the complex case. We discuss some
open problems, and outline directions for further research.
Renato Dias Detecting bifurcation values
Abstract. We discuss algorithms to detect the bifurcation values of polynomial mappings.
Mihai Tibar Lipschitz invariants of holomorphic functions of two variables
Abstract. By combining analytic and geometric viewpoints on the concentration of the curvature of the Milnor fibre, we find some new (discrete) Lipschitz invariants which supplement the (continuous) invariants discovered in 2003. (jointwork with Laurentiu Paunescu)