# Mathematics

Much of the research conducted in this field takes place within a Collaborative Research Centre (SFB): since July 2007, the Faculty of Mathematics has been home to a branch of Transregional Collaborative Research Centre 45 (SFB / TR 45) “Periods, moduli spaces and arithmetic of algebraic varieties. This is a joint research project involving mathematicians from the Universities of Bonn, Mainz and Duisburg-Essen alongside the Max Planck Institute for Mathematics in Bonn. Mainz is responsible for coordination of the project, while mathematicians from Duisburg-Essen account for approximately 40 percent of the proposal volume of roughly two million euros per year. The initial support phase for the SFB / TR runs for four years, with the option of two four-year extensions pending positive evaluation. Part of the SFB is a Research Training Group. The contributors from Duisburg-Essen include the working groups of Gebhard Böckle, Hélène Esnault and Eckart Viehweg (who is the lead coordinator at Duisburg-Essen), and junior scientists Georg Hein, Ho Hai Phúng, and Gabor Wiese. The collaboration with Bonn and Mainz was not entirely a spontaneous decision: no less than three of the contributors from these universities wrote their postdoctoral theses at Duisburg-Essen. The aforementioned working groups and the Institute for Experimental Mathematics help to make the faculty a globally renowned centre for algebraic and arithmetic geometry – a role that SFB / TR 45 is set to intensify. Hélène Esnault has been a member of the German Academy of Sciences Leopoldina since 2008.

The members of SFB / TR 45 have additional third-party funds at their disposal: Hélène Esnault and Eckart Viehweg will have access to unallocated resources from the Leibniz Prize (approx. 300,000 ) up to 2010, and an ERC Advanced Grant has just been awarded (Principal Investigator: Hélène Esnault, 894,000 for five years). These resources have made it possible to gather together a highly active group of mathematicians from various countries.

Members of the SFB have numerous contacts with mathematicians from around the world. This includes cooperation launched in 2008 with the Academy of the Sciences, Hanoi, Vietnam, toeducate Vietnamese mathematics students. Each year, four Vietnamese mathematics students are invited to spend the second year of their Masters studies at the University of Duisburg-Essen. The cooperation may be extended to include doctoral students at a later date and incorporated in the International Graduate School of Mathematics.

The Rüdiger Göbel-Lutz Strüngmann working group concentrates on the interplay betweenalgebra and logic. In the last two years, the group has successfully solved several decades-old problems relating to ring theory (Göbel, Herden, Shelah, J.E.M.S.) and module theory (Shelah, Strüngmann, J.L.M.S.). The research is supported by the DFG with two paid positions as part of a cooperative project with the logicians of the University of Münster. The German-Israeli Foundation for Scientific Research and Development (GIF) is also making funds available for two positions in Essen and a guest programme under a (new) four-year project from January 2009; it also actively supports the longstanding cooperation (financed by prior GIF projects) with logicians and algebraic topologists at the Hebrew University in Jerusalem. The working group has links with partners throughout Western Europe through the European Set Theory Network.