Researchers at the Centre for Advanced Study have contributed to advancing the rapidly developing field of motivic geometry during their year at the Centre.
2020/2021
Motivic Geometry
Motivic Geometry
Mathematics
Principal investigators
Abstract
Motivic Geometry is an amalgam of the classical areas of mathematics called algebra and geometry. The subject was primarily invented to solve long-standing mathematical conjectures via innovative interactions between traditionally different areas of mathematics. Mathematicians are only starting to understand the ramifications of this new perspective initiated in the late 1990s. The CAS project advanced the topics of motivic homotopy theory and its logarithmic version, an emerging algebro-geometric version of Poincare’s conjecture, and quadratically enriched enumerative geometry. Specific milestones in the project include an explicit calculation of the second universal invariant of the motivic spheres, the construction of punctured motivic neighborhoods, stable motivic homotopy types at infinity as a step towards a motivic Poincare conjecture, and complete algebraic counts of enumerative problems. Another development in the project is the ongoing foundational work on logarithmic motivic homotopy theory.
Fellows
Piotr Achinger
Assistant Professor
Institute of Mathematics of the Polish Academy of Sciences
Year at CAS
William Hornslien
PhD Candidate
Norwegian University of Science and Technology (NTNU)
Year at CAS
Ivan Panin
Professor
Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences
Year at CAS
Therese Strand
PhD Candidate
Norwegian University of Science and Technology (NTNU)
Year at CAS
Glen Matthew Wilson
Postdoctoral Fellow
Norwegian University of Science and Technology (NTNU)
Year at CAS