GRK 1821: Cohomological Methods in Geometry

GRK 1821：几何中的上同调方法

基本信息

批准号：
201167725
负责人：
金额：
--
依托单位：
Albert-Ludwigs-Universität Freiburg
依托单位国家：
德国
项目类别：
Research Training Groups
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/201167725?language=en
关键词：
GRK 1821 Cohomological Methods Geometry

项目摘要

The research program is rooted in geometry. The research projects cover a wide range of subjects from mathematical physics to number theory, however, the methods used to study these distinct sets of problems are closely related.The most visible unifying technique used in all our projects is cohomology, a versatile tool central to all geometric disciplines, posed to gain yet more importance in years to come. Nearly all of our projects use Hodge theory, Dirac operators, deformation theory, Lie groups or algebraic geometry. This leads to synergism, of which we are taking advantage. The interplay between abstract algebra and concrete geometry is a Leitmotiv of our research.- The participating researchers work in dierent branches of geometry, yet find a common theme in the methods they use. This set-up is ideal for the training of doctoral researchers. They, as well as our postdocs and advisers prot immensely from the interactions between neighboring fields.- Collaboration with our international partners allows our doctoral researchers to immerse themselves into other communities, establish peer networks, and access further expertise.- The group of applicants consists of five tenured professors and four junior scientists. As planned, there has been a change in the second group. This has led to an expansion of our research profile.- The size of our group is big enough so that fruitful regular seminars and working groups can be organized without putting too much strain on individuals. It is small enough so that researchers know each other well.Our research and qualification program exposes our doctoral researchers to a wide range of research problems while conveying the sense of unity that is central to our science.

研究计划植根于几何形状。研究项目涵盖了从数学物理学到数字理论的广泛主题，但是，用于研究这些不同问题集的方法是密切相关的。我们所有项目中使用的最可见的统一技术是同胞，这是所有几何学学科的多功能工具，在未来几年中却更加重要。我们几乎所有项目都使用霍奇理论，狄拉克操作员，变形理论，谎言组或代数几何形状。这导致了协同作用，我们正在利用它。抽象代数与混凝土几何形状之间的相互作用是我们研究的leitmotiv。-参与的研究人员在几何分支的分支中工作，但在他们使用的方法中找到了一个共同的主题。该设置是培训博士研究人员的理想选择。他们以及我们的博士后和顾问与邻近领域之间的互动非常重要。-与我们的国际合作伙伴的合作使我们的博士研究人员可以将自己沉浸在其他社区中，建立同伴网络并获得进一步的专业知识。按计划，第二组发生了变化。这导致了我们的研究概况的扩大。-我们小组的规模足够大，因此可以组织成果的常规研讨会和工作组，而不会对个人施加太大压力。它足够小，因此研究人员彼此了解。我们的研究和资格计划使我们的博士研究人员遇到了广泛的研究问题，同时传达了对我们科学至关重要的团结感。