MiniWorkshop
Analytic and Algebraic Geometry
May 2627, 2016
Mathematisches Institut  Universität Bern
Program

Jordan groups and birational automorphisms of algebraic varieties
Tatianna BANDMAN (BarIlan University)
Abstract
A group $G$ is called Jordan if there is a positive integer $J=J_G$ such that every finite subgroup
$\mathcal{B}$ of $G$ contains a commutative subgroup $\mathcal{A}\subset\mathcal{B}$ such that
$\mathcal{A}$ is normal in $\mathcal{B}$ and the index $[\mathcal{A}:\mathcal{B}]\leq J$. There is no example of an algebraic
variety with the nonJordan automorphism group. It is known that the group of
birational automorphisms $Bir(X)$ of a projective variety $X$ is Jordan if it is not
uniruled and is not Jordan if $X$ is birational to the direct product of a projective
space with an abelian variety. I will give an introduction to the topic and discuss
the case when variety $X$ is a conic bundle over a nonuniruled variety $Y$ and is not
birational to $Y\times \mathbb{P}^1$. This is a joint work with Y. Zarhin.

$\mathbb{P}^1$bundles over Hirzebruch surfaces
Jérémy BLANC (Universität Basel)
Abstract
In this talk, I will describe the geometry of $\mathbb{P}^1$bundles over Hirzebruch surfaces,
looking in particular at the type of degenerations of the surfaces that one obtain when looking at the pullback of a fibre of the Hirzebruch surface.

Holomorphic automorphisms of the spectral ball
Frank KUTZSCHEBAUCH (Universität Bern )
Abstract

Counterexamples to the complement problem
PierreMarie POLONI (Universität Bern)
Abstract
One of the "challenging problems on affine $n$space" of Hanspeter Kraft's Bourbaki seminar talk was the following.
Given two irreducible hypersurfaces of the complex affine $n$space and an isomorphism of their complements, does it follow that $H_1$ and $H_2$ are isomorphic ?
In this talk, we will give explicit counterexamples to the above complement problem in every dimension $n\geq3$.

Contributions to the theory of density properties for Stein manifolds
Alexandre RAMOS (Universität Bern)
Abstract

Currents associated to attractors in complex dynamics
Johan TAFLIN (Université de Bourgogne)
Abstract
In complex dynamics in several variables, the classical dichotomy between Julia and Fatou sets is insufficient to describe the dynamics.
On the other hand, attractors are fondamental objets in the general theory of dynamical systems. In this talk we will explain how to start the ergodic study
of attractors in the projective space using pluripotential theory. In particular, to each attractor we will associate an attracting current and an equilibrium
measure which give geometric and dynamical information about the attractor.

Categorical action of the braid group of the cylinder
AnneLaure THIEL (Université de Bourgogne)
Abstract
In their seminal work, Khovanov and Seidel have used the polymorphous nature of the usual braid group (ie of finite type A) and hence its various
definitions (diagrammatic presentation, mapping class group...) to construct a categorical action of this group which categorifies its famous
Burau linear representation. The important fact is that this action detects subtle topological properties which ensures its faithfulness unlike
the Burau linear representation.
The aim of this talk is to describe a generalization of their approach to another Artin group, the one of type B  aka the extended braid group of affine type A.
Joint work with Agnès Gadbled and Emmanuel Wagner.
Participants
 S. Baader (Bern)
 T. Bandman (BarIlan)
 R. Bär (Bern)
 A. Dubouloz (Dijon)
 V. Emery (Bern)
 J.P. Furter (Basel)
 M. Hemmig (Basel)
 M. Huber (Bern)
 F. Kutzschebauch (Bern)
 L. Lewark (Bern)
 L. Liechti
 O. Mila (Bern)
 F. Misev (Bern)
 L. MoserJauslin (Dijon)
 J. Taflin(Dijon)
 P.M. Poloni (Bern)
 A. Ramos (Bern)
 Luca Studer (Bern)
 A.L. Thiel (Dijon)
 S. Thomson (Bern)
 S. Zimmermann (Basel)
Schedule
Thursday 
Friday 

BANDMAN 09:4510:45 
KUTZSCHEBAUCH 11:0012:00

Lunch 
Lunch 
TAFLIN 12:4513:45 
POLONI 13:1514:15 
BLANC 14:1515:15 
THIEL 16:0017:00 
RAMOS 15:0016:00 
Social Picnic 
Practical Informations
Organizers
Alexandre Ramos (Bern)
Frank Kutzschebauch (Bern)
Jérémy Blanc (Basel)
Adrien Dubouloz (Dijon)
Sponsors