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

研究培训组的主要目标“代数几何方法在代数，算术和拓扑”是应用结果和代数几何的思想方法纯数学，特别是附近地区的代数，算术和拓扑。这一复杂而强大的理论的使用将被系统地教授给我们的博士生，并将导致优秀的论文。齐性空间、代数簇与群的表示和模空间的代数表示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的研究兴趣，包括代数几何，代数拓扑，算术几何，几何表示理论，模型理论和群论。这涵盖了纯数学的一个重要的和相关的光谱。杜塞尔多夫和伍珀塔尔两地的不同研究小组已经紧密合作了好几年，不同的观点和方法非常有效地相互补充。将现有的专门知识捆绑在一起，就可以培训博士生，而这在所需的深度和广度上，很难单独在每个地点实现。我们的资格认证计划包括，除其他外，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，国外研究访问，以及关键资格的传递。它确保了我们的博士生的最佳支持和发展，并应导致优秀的论文和研究论文。

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.