Nijenhuis geometry and its applications

The Nijenhuis geometry project was started in 2017 by A.Yu.Konyaev, A.V. Bolsinov, and V.S.Matveev. The new geometry tackles a wide variety of questions, including the local description of normal and seminormal forms in regular points, singularities, and global questions. The latter includes cohomologies, topology, etc.
It turns out that the applications of Nijenhuis geometry are related to the companion objects. This yields many interesting geometric questions. The applications include algebra, integrable systems, differential geometry and mathematical physics.
The talk presents an overview of the Nijenhuis geometry over last 8 years.