The ERC project QUADAG

Professor Marc Levine has been awarded the ERC Advanced Grant on quadratic refinements in algebraic geometry for a five-year research project in the field of motivic homotopy theory. Levine has been an influential contributor to this field for many years. His project is based on the combination of methods in algebraic geometry with those of homotopy theory. The algebraic foundation of the former ensures that a good local understanding of objects always facilitates global conclusions through long-distance effects. In the latter, geometry facilitates highly flexible deformations at the local level without global effects. A combination of these opposed approaches, which were originally developed to solve issues in number theory, has been applied to many fields of mathematics, including mathematical physics.

For his ERC project, Professor Levine has developed new methods that open up additional fields of application.  His goal is to use quadratic refinements to establish new connections between real algebraic geometry, tropical geometry, singularities and objects in number theory.

The project has already attracted four new international members – two post-doctoral researchers and two doctoral candidates – to the Essen-based research group. It originated from the DFG Priority programme 1786, ‘Homotopy Theory and Algebraic Geometry’, whose researchers from the eponymous areas have been working to find new connections such as those studied in the new ERC project since 2015. Multiple research groups at our faculty are involved in this programme. Over the reporting period, we were able to organise two international conferences and one international doctoral research school on the topic of motives and stacks in Essen.