SPP 1786: Homotopy Theory and Algebraic Geometry

Basic data for this project

Description

The Priority Programme 1786 in Homotopy Theory and Algebraic Geometry builds upon recent developments in two central pillars of modern mathematics, algebraic geometry and homotopy theory, bringing together mathematicians working in these areas to encourage interactions among researchers and break down the classical boundaries between homotopy theory and algebraic geometry. Algebraic geometry studies the solution sets of algebraic equations, applying methods from algebra, analysis and topology, and has wide-ranging applications to other branches of mathematics as well as to physics and engineering. Homotopy theory is an important branch of topology, dealing with properties of spaces that are preserved in continuous families and studying them through algebraic invariants. This Priority Programme is based on several areas of interaction between these two fields:Motivic homotopy theory. Derived algebraic geometry. Differential homotopy theory and Arakelov Theory. Equivariant homotopy theory and its links to motivic homotopy theory.