Gereon Quick (NTNU): Topological and arithmetic invariants for algebraic cobordism cycles

Calculating the residues for rational integrals in complex variables is a classical problem in mathematics. It is directly related to questions on algebraic cycles, their cohomology classes, and the Abel-Jacobi map. I will discuss the analogs of these questions for algebraic cobordism cycles. In particular, I will present new versions of an Abel-Jacobi map, a regulator map and Arakelov arithmetic cobordism. This in part joint work with Michael Hopkins.