GRK 1821: Cohomological Methods in Geometry

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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.