This project studies motivic homotopy theory, a relatively new subject that allows us to utilize algebraic topology methods to understand the objects of interest in algebraic geometry. The motivic theory has had several spectacular successes in resolving deep mathematical problems. Spheres are simple yet essential objects of study in geometry, and they are considered in the realm of algebraic geometry. One of the central questions is the classification of all possible mappings of a high-dimensional sphere onto a lower dimension sphere.
Motivic Geometry is an interdisciplinary high-risk project in the mathematical sciences. By bringing together world-leading experts in motivic homotopy theory, affine algebraic geometry and enumerative geometry, we aim at reaching decisive results and shape the future research directions in these subjects. The inflection point we find ourselves at today consists of a deepening of the creative interplay between these areas, with dramatic and quite unexpected connections such as a motivic Poincaré conjecture coming into focus.
This is a project funded of RCN. The research aims at formulating and solving ground-breaking problems in motivic homotopy theory. As a relatively new field of research this subject has quickly turned into a well-established area of mathematics drawing inspiration from both algebra and topology.
Research program at Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, Djursholm, Sweden.