Project Details
Projekt
GRK 2553: Symmetries and classifying spaces: analytic, arithmetic and derived
Subject Area
Mathematics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 412744520
The study of symmetries and classification of geometric objects lies at the heart of mathematics and of algebraic geometry in all of its flavors: classical algebraic geometry, complex geometry, arithmetic geometry, derived algebraic geometry and other areas at the border between algebraic geometry, analysis and topology. This very active subject has made substantial progress in the past years, e.g., the theory of perfectoid spaces, a better understanding of the Langlands programme and of the Birch and Swinnerton-Dyer conjecture, and new results on the minimal model programme. New tools are developing quickly and further breakthroughs can be expected in the future. For young mathematicians this is a promising field in which to start one's career. In view of the difficulty and the breadth of the methods, it is particularly useful for doctoral researchers to study and work in an environment where expertise in many of the different approaches to the subject is available. At Essen, we can offer such a stimulating environment, supporting doctoral researchers in the transitional phase between student and researcher, and enabling them to enter a fascinating area of mathematics. Our research focuses on groups and classifying spaces in a broad sense and includes complex and p-adic Lie groups, algebraic groups and Galois groups, their actions on varieties and related spaces and representation theoretic questions with a link to geometric problems, as well as moduli spaces, deformation spaces, and classifying spaces in the strict sense. Symmetries and classifying spaces are often closely linked. The projects in the second funding period build on the results established and the connections between our research groups strengthened in the first period, as well as other recent developments in this field of research. In the qualification programme, our goal is to provide doctoral researchers with enough freedom to develop their own ideas and become, step by step, more independent, and to provide enough guidance to promote an effective use of their time and to ensure their work has a significant perspective going beyond the PhD thesis, in an environment that allows them to concentrate fully on mathematics.
DFG Programme
Research Training Groups
Applicant Institution
Universität Duisburg-Essen
Spokesperson
Professor Dr. Jochen Heinloth
