# Welcome to Sonderforschungsbereich/Transregio 45

Periods, moduli spaces and arithmetic of algebraic varieties

## Summary

The SFB/TRR has its focus on research about Periods, Moduli Spaces and related aspects of the Arithmetic of Algebraic Varieties. These are very active research areas, directed towards central questions in the theory of algebraic varieties. Some of the most exciting developments take place where arithmetic and geometry meet, and where one is looking for new methods, building yet unknown bridges between different points of view. Many of the algebraic varieties studied in our projects are relevant to other sciences like mathematical physics or computer science.

## Project Areas

### Third Funding Period (2015-2019):

- M02: Motives and periods
- M03: Galois representations, finite and mixed characteristics
- M04: Rational points
- M05: Periods and period domains
- M06: Shimura varieties
- M07: Calabi-Yau categories
- M08: Moduli spaces, symplectic and Calabi-Yau manifolds

### Second Funding Period (2011-2015):

- M01: Fundamental groups
- M02: Motives and periods
- M03: Galois representations, finite and mixed characteristics
- M04: Rational points
- M05: Periods and period domains
- M06: Shimura varieties
- M07: Calabi-Yau categories
- M08: Moduli spaces, symplectic and Calabi-Yau manifolds

### First Funding Period (2007-2011):

- Motives, Periods and Arithmetic of Varieties
- Structure of Certain Period Domains
- Geometry and Moduli of Special Manifolds

## Participating Departments and Institutes

The following departments and institutes participate at this SFB.

- Institut für Mathematik, Fachbereich 08, Johannes-Gutenberg-Universität, Staudingerweg 9, 55099 Mainz
- Mathematisches Institut der Rheinischen Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn and Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn
- Fachbereich Mathematik, Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen