# Summer School and Workshop: Differential Forms on Singular Complex Spaces

Date: June 30 - July 04, 2014

Time: The event will start on Monday at 8 a.m. and end on Friday around 4 p.m.

Venue: Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

Organizers: Dariush Ehsani (Wuppertal), Ingo Lieb (Bonn), Jean Ruppenthal (Wuppertal)

Mathematical Objectives: Differential forms are an indispensable tool to study the geometry and topology of complex manifolds; particularly the $L^2$-theory and integral formulas for the $\overline{\partial}$-complex are of great importance. In the presence of singularities, the influence of differential forms on the local and global geometry of a variety is much less explored. However, recently, there has been considerable progress in the topic from different sides. On the one hand, from the perspective of complex geometry, Greb-Kebekus-Peternell and others have created a coherent theory for holomorphic differential forms on singular spaces which is particularly applicable in the context of the minimal model program. On the other hand, concerning the development of analytic tools (transcendental methods), Ovrelid-Vassiliadou and others have proved many interesting results on the $L^2$-regularity of the $\overline{\partial}$-equation on singular spaces and found a way to describe the $L^2$ cohomology by means of resolution of singularities. Moreover, Andersson-Samuelsson have developed Koppelman formulas for the $\overline{\partial}$-complex on singular spaces yielding a local Dolbeault-Grothendieck lemma for such spaces.

Aim of the Summer School and Workshop: Our intention is to bring together experts in these active areas to a summer school in order to foster collaboration and exchange of ideas with a special focus on young mathematicians. We expect that it will be fruitful to present all these new interesting developments in a coherent context. The objectives of the summer school are to lay a solid foundation essential for research on singular complex spaces, to connect various approaches to this area through a broad perspective, and to introduce contemporary and ongoing research in this field. The intended audience are graduate students, post-docs, and young researches in related areas.

The Event will consist of a series of three mini-courses in the morning and several complementary invited lectures by other experts in the field in the afternoon.

The Mini-Courses:

* Reflexive differential forms on singular spaces (Stefan Kebekus, Freiburg),

* $L^2$-theory for the $\overline{\partial}$-operator on singular spaces (Nils Ovrelid, Oslo),

* Koppelman formulas on singular spaces (Mats Andersson, Goteborg)

Mini-courses

Social Dinner:

On Thursday July 3, at 7:30pm we will be having a social dinner at the Bierhaus-Machold in Altstadt. We will meet at 7:00pm at the entrance of the Math Department (Endenicher Allee 60) and walk together to the restaurant. If you plan to attend please don't forget to sign your name on the dinner sign-up sheet. Each participant will pay his/her own costs at the restaurant directly.

Map to Bierhaus-Machold

 Social_Dinner.pdf