GRK 2240: Algebro-geometric methods in algebra, arithmetic and topology

“代数、算术和拓扑学中的代数几何方法”研究训练组的主要目标是将代数几何的结果和思想方法应用到纯数学中，特别是应用到代数、算术和拓扑的邻近领域。使用这一复杂而强大的理论将系统地教授给我们的博士生，并将导致优秀的论文。齐次空间、与群表示有关的代数簇和箭图表示的模空间仍然是研究的中心课题。新的研究课题包括奇点、算术群和Chow-Witt群。这反映了参与研究人员对代数几何、代数拓扑、算术几何、几何表示论、模型论和群论的研究兴趣。这涵盖了纯数学的一个重要且相互关联的范围。杜塞尔多夫和伍珀塔尔两个地点的不同研究小组已经密集合作多年，不同的观点和方法非常有效地相辅相成。现有专业知识的结合使博士生的培训成为可能，而在所需的深度和广度上，仅在每个地点都很难做到这一点。我们的资格认证计划包括双重监督、定期进度评估、每周RTG日、暑期学校、客座研究人员计划、海外研究访问以及关键资质的传授。它确保了我们博士生的最佳支持和发展，并应该导致优秀的学位论文和研究论文。

The main goal of the research training group "Algebro-Geometric Methods in Algebra, Arithmetic and Topology" is the application of results and ways of thought of algebraic geometry to pure mathematics, and in particular to the nearby areas of algebra, arithmetic and topology. Usage of this sophisticated and powerful theory will by taught systematically to our doctoral students and should lead to outstanding dissertations. Homogeneous spaces, algebraic varieties in connection with representations of groups and moduli spaces of quiver representations remain central topics of study. New research topics include singularities, arithmetic groups and Chow-Witt groups. This reflects the research interests of the participating researchers, which lie in algebraic geometry, algebraic topology, arithmetic geometry, geometric representation theory, model theory and group theory. This covers an important and connected spectrum of pure mathematics. The different research groups at the two locations in Düsseldorf and Wuppertal have already been working together intensively for several years, and the different points of view and methods supplement each other very effectively. The bundling of the available expertise allows a training of doctoral students, which, in the desired depth and broadness, would be difficult to achieve at each of the locations alone. Our qualification programme includes, among other things, double supervisions, regular progress assessment, a weekly RTG day, summer schools, a scheme for guest researchers, research visits abroad, and the conveyance of key qualifications. It ensures an optimal support and development of our doctoral students, and should lead to outstanding dissertations and research papers.