複素幾何セミナーの記録

１月１７日（水）１５：００〜１８：００（時間がいつもと違います）
修士論文発表会の練習


１１月２２日（水）１５：００〜１８：００（時間がいつもと違います）
修士論文中間発表会


５月１７日（水）１６：３０〜１７：３０
Falko Gauss氏 (Universität Manheim)
The moduli space of marked singularities

Abstract:
The moduli space of marked singularities was introduced by Claus
Hertling in 2010 and parameterizes μ-homotopic isolated hypersurface
singularities equipped with certain markings. This moduli space can be
understood either as a global μ-constant stratum or as a Teichmüller
space of singularities. The additional marking allows one to formulate
the conjecture on the analytic behavior of singularities within a
distinguished μ-homotopy class in terms of a Torelli type problem in a
very efficient way. In my talk I will discuss the history of this
problem and introduce carefully the notion of a marked singularity.
Secondly, I will speak about recent results on this Torelli type
problem for bimodal series singularities. There the moduli space shows
some unexpected behaviour.


４月１９日（水）１６：３０〜１７：３０
Frank Kutzschebauch氏 (Universitaet Bern)
The Linearization Problem

Abstract: Given a reductive group $G=K^\C$ ($K$ maximal compact subgroup) acting algebraically/holomorphically on $\C^n$. Is there an algebraic / holomorphic change of variables which conjugates the action of $G$ into a linear action?
We review the history mainly of the holomorphic part of the problem. Then we discuss the counterexamples to the problem found by Derksen and the speaker and explain recent positive results of Larusson, Schwarz and the speaker.


４月１２日（水）１６：３０〜１７：３０＠１１号館２０１教室
（いつもと場所が違います）
Frank Kutzschebauch氏 (Universitaet Bern)
The density property

Abstract: The density property d.p. is a precise notion for having a big group of holomorphic automorphisms. It was introduced by Varolin in the 1990s as a successful attempt to generalize the famous Andersen-Lempert Theorem (saying that finite compositions of triangular and affine automorphisms form a dense subgroup in the holomorphic automorphism group of $\C^n$) to other manifolds. We explain the consequences of d.p., give examples of manifolds having d.p. and an overview of applications of the theory to natural geometric questions.