Paul Goerss

Paul Goerss is Professor of mathematics at Northwestern University, USA. He works in homotopy theory, the branch of algebraic topology which studies spaces and continuous maps up to continuous deformation. 

Many problems in geometry and topology begin with questions in homotopy theory. A sample open question is to calculate the homotopy classes of maps between spheres. This is impossible to answer at the moment, but progress can be tested against this question.

In chromatic stable homotopy theory, the main innovation is the introduction and exploitation of small topological resolutions. If algebraic geometry is geometry built from commutative rings, then derived algebraic geometry is built from commutative ring objects in some category amenable to homotopy theory. This is a large and rapid-developing field, with strands in many directions. One developed technique, now known as Goerss-Hopkins obstruction theory, has had a number of successes, and has opened up new directions such as the study of topological modular forms which, in turn, was one of the main examples that led to the full development of derived algebraic geometry.

Professor Goerss is hosted by Professor Hans-Werner Henn at the Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS.