Algebraic Geometry and Arithmetic

The research topics of the Essen Seminar for Algebraic Geometry and Arithmetic (ESAGA) centre on Algebraic Geometry, Number Theory and Algebraic Topology. Among the specific research interests of its members are motivic homotopy theory, algebraic cobordism, questions about rational points, the classical and the p-adic Langlands program, Shimura varieties, lattices and theta series, algebraic stacks, moduli spaces, classification theory of complex-algebraic varieties, L-functions and the representation theory of p-adic Lie groups, Iwasawa theory, topology and analysis on singular spaces.

The many connections between these topics lead to an intense exchange between the research groups of the Essen Seminar. The Transregio-Collaborative Research Centre 45 “Moduli spaces, periods, and arithmetic of algebraic varieties” (Mainz/Bonn/Essen) was extended for the second time in 2015 and is now in its third funding period. The significance of this field of research has been further underlined by the Fields Medal, which was awarded in August 2018 to the CRC member Prof. Peter Scholze.

The CRC enables the Essen Seminar to carry out a multitude of activities, includes a number of positions for PhD students and postdocs, and increases the possibilities for exchange through visiting researchers.

The DFG Priority Programme 1786 “Homo­topy theory and algebraic geometry”, which was initiated and is coordinated by Prof. Marc Levine, entered its second funding period in 2018. In this programme, new developments connecting algebraic topology and algebraic geometry are investigated at universities all over Germany. Since its start in May 2015, the programme has already seen a large number of conferences and workshops, several among them taking place in Essen.

For several years, Essen has been one of the venues of the “Joint Seminar on Complex Algebraic Geometry and Complex Analysis”, organised by the complex geometry research groups at the Universities of Bochum, Duisburg-Essen (Greb research group), Cologne, and Wuppertal. It is a platform for talks both by invited guests (in the last two years from the Universities of Cambridge, Hamburg, Oxford, and Paris, among others) and by speakers from the organising universities, as well as for discussions among the members of the research groups involved.

In the two years of the report, two Heisenberg fellows of the German Research Foundation (DFG) have been working at the Essen Seminar. They are PD Dr. Andre Chatzistamatiou (April 2017–October 2018) and PD Dr. Andreas Nickel (since May 2017).

The Algebraic Geometry and Complex Analysis and Number Theory sections of the annual meeting of the German Association of Mathematicians (DMV) in 2018 in Paderborn were chaired by Prof. Jochen Heinloth and Prof. Jan Kohlhaase together with colleagues from Bochum and Münster.

Within the WISNA programme for the advancement of young scientists, a call for a Junior Professorship for Algebra and Number Theory (W1 with tenure track as per W2) was announced in the Faculty of Mathematics. The appointment has been offered to the top short-listed candidate, and the position will hopefully be filled before the summer term of 2019.

In November 2018, the German Research Foundation positively evaluated a draft proposal for a Research Training Group and the proposal to establish the group is planned for submission in the spring of 2019.

As usual, the Essen Seminar was host to a large number of international researchers. Paul Arne Østvær from the University of Oslo was awarded one of the Friedrich Wilhelm Bessel Research Prizes of the Alexander von Humboldt Foundation in April 2017 to facilitate visits to Essen (Prof. Marc Levine’s research group) and to the University of Osnabrück. He has already visited Essen twice, and further visits are planned. Further guests in the two years of the report included Henri Darmon (McGill University, Montreal), Christian Haesemeyer (University of Melbourne), Bharathwaj Palvannan (University of Pennsylvania), and Marco Seveso (Università degli Studi di Milano).

Members of ESAGA collaborated with mathematicians from all over the world, for instance with Jarod Alper (University of Washington), David Burns (King’s College London), Mark de Cataldo (Stony Brook), Pierre Colmez (CNRS Paris), Henri Darmon (Mc Gill University, Montreal), Matthew Emerton (University of Chicago), Toby Gee (Imperial College, London), Daniel Halpern-Leistner (Cornell), Xuhua He (University of Maryland), Henry Johnston (Exeter), Luca Migliorini (Bologna), Julius Ross (University of Illinois at Chicago), and Richard Wentworth (University of Maryland).

The Essen Seminar is a member of the international ALGANT network, a high-profile Master’s programme which introduces students to research questions at an early stage.