The research activities of the Essen Seminar for Algebraic Geometry and Arithmetic (ESAGA) include several interrelated areas of algebraic ­geometry, arithmetic and algebraic topology. Specific research interests include motivic homotopy theory, algebraic cobordism, questions concerning rational points, the Langlands program, Shimura varieties, varieties of quiver representations, lattices and theta series, moduli stacks of vector bundles and principal bundles, p-adic ­local Langlands theory and the representation theory of p-adic Lie groups.
Collaborative Research Centre/Transregio SFB/TR 45, “Moduli spaces, periods and arithmetic of algebraic varieties”, with Bonn and Mainz was successfully extended to its second four-year funding period. The SFB enables ESAGA to fund a wide variety of research activities, ­primarily by offering positions for doctoral students and post-doctoral researchers, as well as aiding collaborative activities with funding for visits by outside researchers and for members of the research groups to visit other research ­institutions. The renewal of the SFB by the DFG therefore marks a particularly important step forwards for ESAGA.
In addition to the ongoing support from the DFG, Professor Marc Levine continues to receive funding from the Humboldt Foundation through his Humboldt Professorship. Currently six ­postdocs and four doctoral students are being funded in this way. Professor Ulrich Görtz is participating in DFG Priority Programme 1489 “Algorithmic and experimental methods in algebra, geometry and number theory”.
Two new professors have joined the Essen Seminar: Professor Jochen Heinloth from the University of Amsterdam and Professor Vytautas Paskunas from the University of Bielefeld arrived in Essen at the beginning of the winter semester 2011/12. Both professors have since become involved in Transregio Collaborative Research Centre SFB/TR 45 following successful subsequent applications.
As is customary for the Essen Seminar, it has been host to a large number of  international guest researchers on extended visits. A graduate student exchange programme with Northeastern University has been launched, under which three students have been hosted so far.
Members of ESAGA have collaborated with mathematicians throughout the world, including Spencer Bloch (University of Chicago), Matthew Emerton (University of Chicago), Oscar Garcia-Prada (ICMAT, Madrid), Olivier Wittenberg (ENS, Paris), Xiaotao Sun (Beijing) and Johannes Nicaise (Leuven).
Regrettably for the department, the scientific quality of ESAGA members has been confirmed by a number of external appointments, with Moritz Kerz accepting an offer from the University of Regensburg and Junior Professor Gabor Wiese taking up a position at the University of Luxembourg. In the 2012/2013 winter semester Professor Hélène Esnault accepted an offer from the Freie Universität Berlin and became its first Einstein Professor. The department is sorry to see them go and wishes them the very best in their new posts.
The research group of Professor Günter Törner has for several years now been pursuing a number of interesting topics, including research in pure mathematics in the area of non-commutative algebra and valuation theory, applied development projects with companies in the area of discrete mathematics, in particular scheduling theory, and mathematical sociology studies on mathematics in society, in particular analysis of students dropping out of university in mathematics. ­Professor Törner is the Chair of the Committee of Education of the European Mathematical ­Society (EMS) and together with the president of Berlin University for Professional Studies (DUW) heads Department A of the German Centre of Mathematics Teacher Education (DZLM).
Since April 2012 he has been one of the two good scientific practice ombudsmen at the University of Duisburg-Essen.