The annual meeting of the Deutsche Mathematiker-Vereinigung 2015 was the fourth such meeting to be held in Hamburg after previous meetings in 1901, 1928 and 1979. It was hosted by the Department of Mathematics of the University of Hamburg from the 21st to the 25th of September 2015. The organisers collaborated with the Dansk Matematisk Forening during the composition of the scientific programme.

With about 900 participants it was the biggest single DMV-meeting so far (although some joint meetings of the DMV with other mathematical societies have been larger). It required not only the full capacity of lecture halls and seminar rooms at the main building of the University of Hamburg but also the devoted activity of many individuals including the organizing committee (Charlotte Becker (née Schulze), Alexander C. Block, Andrea Blunck, Vicente Cortés, Alexander Haupt, Stefan Heitmann, Michael Hinze, Ralf Holtkamp, Nick de Hoog, Philine Kortmann, Ruslan Krenzler, Ulf Kühn, Reiner Lauterbach, Benedikt Löwe (chair), Janja Nahrstaedt, Hendrik Niehaus, Sonja Otten, Birgit Richter) and the programme committee (Volker Bach (Braunschweig), Christian Bär (Potsdam), Andrea Blunck (Hamburg), Vicente Cortés (Hamburg), Vagn Lundsgaard Hansen (Kungens Lyngby, Denmark), Michael Hinze (Hamburg), Ulf Kühn (Hamburg), Reiner Lauterbach (Hamburg), Benedikt Löwe (Amsterdam, The Netherlands & Hamburg, chair), Birgit Richter (Hamburg)).

We are very happy to present in this volume some of the scientific ideas interchanged at the meeting. The volume includes a selection of articles by key note speakers and speakers of sections and minisymposia. We are very grateful to the authors for presenting their work.

Hamburg, 12th of September 2016

Vicente Cortés, Birgit Richter