TRR 45:  Periods, Moduli Spaces and Arithmetic of Algebraic Varieties

Subject Area Mathematics
Term from 2007 to 2019
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 30164218
 

Project Description

Periods, moduli spaces and related aspects of the arithmetic of algebraic varieties are central research themes inside the SFB/Transregio 45. These topics and some of the most exciting recent developments around them touch central questions in the intersection of arithmetic and geometry. Although algebraic geometry and number theory have coexisted for a long time, the close connection between these two areas that we now enjoy began only in the twentieth century. The development of schemes and general cohomology theories, as well as the theory of motives, provided a common framework for both. A prominent example for such interplay is Wiles' proof of the Fermat conjecture, which uses the geometry of elliptic curves and their Tate modules to prove a genuinely arithmetic statement. In our research we aim to develop further tools relating arithmetic and geometry, and hope to build as yet unknown bridges between the two different points of view. We have chosen a selected group of PIs with similar common research interests so that a close interaction would be possible. Our main goal besides advancing our understanding of this interplay is to motivate young mathematicians to enter this fascinating area of research and enable them to see the geometric and arithmetic perspectives from the beginning of their studies.Many of the main research topics have been carried over from the first and second funding period. In addition, we have added several new research topics, e.g., p-adic representations and L-functions, local Shimura varieties and diophantine problems, cubic 4-folds and related questions, geometric representation theory, Quiver Schur Algebras, Jacobian Algebras, K-theory of stacks, Mumford-Tate domains, elliptic motives, several aspects of birational geometry and the geometric Langlands correspondence.
DFG Programme CRC/Transregios
International Connection Vietnam

Completed projects

Applicant Institution Johannes Gutenberg-Universität Mainz
Co-Applicant Institution Rheinische Friedrich-Wilhelms-Universität Bonn; Universität Duisburg-Essen
Campus Essen (aufgelöst)
Participating Institution Max-Planck-Institut für Mathematik
Spokespersons Professor Manuel Blickle, Ph.D., since 1/2017; Professor Dr. Stefan Müller-Stach, until 12/2016