# Mathematics

## Algebra/Algebraic Geometry/Number Theory

Research at the Essen Seminar for Algebraic Geometry and Arithmetic (ESAGA) covers topics of algebraic geometry, arithmetic and algebraic topology. Representative research interests include motivic homotopy theory, algebraic cobordism, rational points, the Langlands program, Shimura varieties, lattices and theta series, algebraic stacks, moduli spaces, p-adic local Langlands theory, L functions, and representation theory of p-adic Lie groups.

The many connections between these different topics create a lively exchange between the research groups at the Essen Seminar.

The Transregio Collaborative Research Centre 45 “Moduli spaces, periods and arithmetic of algebraic varieties” (Mainz/Bonn/Essen) is currently in its second funding period. It has made way for a variety of research activities, especially through doctoral and postdoctoral posts, and scientific exchange with visiting scholars at the Essen Seminar. Prof. Ulrich Görtz and also Ishai Dan-Cohen from Prof. Jochen Heinloth’s research group are furthermore taking part in the DFG Priority Programme SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”.

The Priority Programme initiated by Prof. Marc Levine, SPP 1786 “Homotopy theory and algebraic geometry”, has been approved by the DFG and will commence its work with Prof. Levine as coordinator in 2015.

The Essen Seminar again hosted a large number of international scholars for extended visits to Essen. In the summer semester of 2014, a special semester was held with the support of the Humboldt professorship of Prof. Marc Levine on the topic of motivic homotopy theory, which included five lecture series by international visiting scientists and an international workshop on “Motivic homotopy groups of spheres”. Prof. Jerzy Weyman (University of Connecticut) also joined Prof. Levine’s research group for several months of research funded by a Humboldt Senior Research Award.

Over the past two years, the Essen Seminar has gained three new professors, which means that all the posts in Algebra are now occupied in the Faculty. Prof. Massimo Bertolini joined the Essen Seminar from the University of Milan in the winter semester 2013/14. Prof. Jan Kohlhaase followed in 2014, and Prof. Daniel Greb has also taken up his post as from winter semester 2014/15. All three are already involved in the application for the third funding period of the Collaborative Research Centre.

The members of ESAGA have worked with mathematicians from all over the world, including Pierre Colmez (CNRS Paris), Henri Darmon (McGill University, Montreal), Oscar Garcia-Prada (CSIC Madrid), Tamas Hausel (EPFL Lausanne), Xuhua He (University of Maryland), Julius Ross (Cambridge), and Jerzy Weyman (University of Connecticut).

**Awards and Distinctions:**

- Prof. Marc Levine was accepted into the National Academy of Sciences Leopoldina in 2013.
- Dr. André Chatzistamatiou received a Heisenberg Fellowship, which he is taking up at the Max Planck Institute for Mathematics in Bonn.

**Conferences in Essen:**

- As part of the special semester on algebraic homotopy theory, a workshop on “Motivic Homotopy Groups of Spheres” was held in June 2014 with participants from countries including India, Japan, Russia, Sweden and the USA.