Seminar on Complex and Symplectic Geometry


S. Ivashkovitch, G. Marinescu, N. Shcherbina

Monday, 3 pm, Hörsaal of the Max Plank Institute, Bonn

Sergey Ivashkovich, Reflection Principle in Non-integrable Structure

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

Jean Ruppenthal, About the d-bar-equation on singular Stein spaces

Abstract: One of the most important setups for considering the Cauchy-Riemann 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 d-bar-equation on M, and to determine the regularity of the d-bar-equation on M. In this talk, we will give a little survey about these two problems, addressing methods, results, perspectives and applications.

Stefan Nemirovski, Lagrangian Klein bottles in R^2n

Abstract: It will be shown that the n-dimensional Klein bottle admits a Lagrangian embedding into R^2n if and only if n is odd.

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 Calabi-Yau theorem in the projective world.

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 non-squeezing 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 long-sought 7- and 8-packings 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.

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.

Nikolai Tarkhanov : An explicit Carleman formula for the Dolbeault cohomology

George Marinescu

letzte Änderung am

8. Dezember 2008