Global Homotopies for HKR Theorems in Differential Geometry

Explore a mathematical lecture that delves into a novel proof approach for the Hochschild-Kostant-Rosenberg (HKR) Theorem in Differential Geometry, focusing on the development of explicit global homotopies through symbol calculus and van Est-double complex methods. Learn how the HKR morphism's role in deformation theory and quantization can be understood through this new perspective, which offers advantages over traditional local proofs. Discover applications of this innovative proof strategy to various mathematical scenarios, including submanifolds, surjective submersions, and equivariant versions for both Lie group and Lie algebra actions. Presented as part of the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute for Mathematics and Physics, this 55-minute talk provides a fresh understanding of a fundamental theorem in differential geometry while demonstrating its broader applicability to more structured mathematical situations.