The goal of geometry is to investigate the properties of manifolds (spaces and figures). In geometry up to high school, we focus on quantities (invariants) such as length, area, and angle, but there are other invariants that are suitable for investigating properties. While invariants are quantities that should be observed instead of length and the like, they can also be regarded as instruments like microscopes and telescopes in the sense of their use for investigating the properties of manifolds. In this view, it is also an important goal to raise the performance of observation.
One important invariant is cohomology. Originally found as the dual of homology, which is an invariant for examining topological properties, cohomology also reflects the analytic properties of manifolds. In particular, the cohomology theory has been extended and refined to many varieties in order to capture interesting properties of algebraic varieties. One of the streams of research has led to twistor D-modules through the theory’s extension to D-modules and refinement by Hodge and twistor structures. At the symposium, the lecturer will introduce some aspects of the spread of cohomology theory.