**多复变与复几何学术年活动**

**Some Topics in Several Complex Variables**

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**1. Title: **Some open problems concerning Stein spaces (I)

—Open problems concerning Stein spaces, a first survey.

**Speaker:** *Prof. Klas Diederich (University of Wuppertal).*

**Time:** April 29 (Wednesday), 15:00—17:00.

**Place:** Room 210 of South Building.

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** Abstract: **The theory of Stein manifolds is well understood. In contrast there are still many open questions for singular Stein spaces, even if they only have isolated singularities. We will give a survey of the situation in the more or less degenerate case. The most important area of open questions concerns the local Steiness problem. It is very much related to the Problem of hypersurface sections, which can be understood as an effort to solve the Levi problem by induction over the dimension. We will however sketch the idea of a counterexample to the hypersurface problem, due to M.Colţoiu and K. Diederich. It gives rise to ask for several important generalizations.

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**2. ****Title: **Some open problems concerning Stein spaces (II)

—Unions and intersections of Stein spaces.

**Speaker:** *Prof. Klas Diederich (University of Wuppertal).*

**Time:** May 4 (Monday), 15:00—17:00.

**Place:** Room 913 of South Building.

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** Abstract: **The theory of Stein manifolds is well understood. In contrast there are still many open questions for singular Stein spaces, even if they only have isolated singularities. We will give a survey of the situation in the more or less degenerate case. The most important area of open questions concerns the local Steiness problem. It is very much related to the Problem of hypersurface sections, which can be understood as an effort to solve the Levi problem by induction over the dimension. We will however sketch the idea of a counterexample to the hypersurface problem, due to M.Colţoiu and K. Diederich. It gives rise to ask for several important generalizations.

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**3. Title: **Some open problems concerning Stein spaces (III)

—The local openness problem (The Levi problem) and the problem of

hypersurface sections.

**Speaker:** *Prof. Klas Diederich (University of Wuppertal).*

**Time:** May 8 (Friday), 9:00—11:00.

**Place:** Room 913 of South Building.

** Abstract: **The theory of Stein manifolds is well understood. In contrast there are still many open questions for singular Stein spaces, even if they only have isolated singularities. We will give a survey of the situation in the more or less degenerate case. The most important area of open questions concerns the local Steiness problem. It is very much related to the Problem of hypersurface sections, which can be understood as an effort to solve the Levi problem by induction over the dimension. We will however sketch the idea of a counterexample to the hypersurface problem, due to M.Colţoiu and K. Diederich. It gives rise to ask for several important generalizations.