14.04.2008

Sergey Ivashkovich, Reflection Principle in Nonintegrable Structure
Abstract: We shall give a direct analog of the classical Schwarz Reflection Principle
for pseudoholomorphic curves in real analytic almost complex manifolds.



28.04.2008

Jean Ruppenthal, About the dbarequation on singular Stein spaces
Abstract: One of the most important setups for considering the CauchyRiemann equations
on a singular Stein space X is to simply work on the complex manifold M consisting of the regular part of X,
which is in general not a Stein space any more.
In this situation, two main topics of current research are
to identify the obstructions for solving the dbarequation on M,
and to determine the regularity of the dbarequation on M.
In this talk, we will give a little survey about these two problems,
addressing methods, results, perspectives and applications.



5.05.2008

Stefan Nemirovski, Lagrangian Klein bottles in R^2n
Abstract: It will be shown that the ndimensional Klein bottle
admits a Lagrangian embedding into R^2n if and only if n is odd.



2.06.2008

Julien Keller, Canonical neighborhood of a divisor
Abstract: Let D be a divisor of a smooth complex projective manifold M
and L be an ample line bundle on M. We consider the Bergman kernel
of sections of high tensor powers L^k that vanish on D at order k?.
This can be seen as a function on M depending on k. Its asymptotic
when k tends to infinity has a natural geometric interpretation. We obtain
the construction of a canonical neighborhood of D. Another consequence
is a weak version of the CalabiYau theorem in the projective world.



9.06.2008

Ingo Wieck : Symplectic Tunnelling, or how to stack symplectic oranges
Abstract: After roughly 400 years of research, the optimal method of stacking oranges or cannon balls has recently been determined. But what if the oranges are symplectic?
From Gromov's fundamental nonsqueezing theorem in 1985 to McDuff's ellipsoid embedding transformation in 2008, many results underline the significance of the symplectic ball packing problem. Its solutions can often be implicitly computed, but their geometric realization has long lagged behind.
After recalling and motivating the ball packing problem, my talk will shortly explain some explicit packing methods called "deformation", "wrapping" and "folding". Then a new method called "tunnelling" is introduced and applied to construct many new optimal packings, among them the longsought 7 and 8packings of B4.
A key feature of the topic is that its explicit geometric ideas require no formulas. Since I describe all problems, methods and solutions in pictures, my talk can easily be followed without any previous knowledge on symplectic geometry.



10.11.2008

Frank Kutzschenbauch : Holomorphic factorization of maps into the special linear group
Abstract: In the talk we explain a complete solution to Gromov's Vaserstein Problem.
This is a joint work with B. Ivarsson.



8.12.2008

Nikolai Tarkhanov : An explicit Carleman formula for the Dolbeault cohomology




letzte Änderung am
8. Dezember 2008