Lagrangian submanifolds, Algebraic K-theory, and Quantum Physics

Project funded by Swedish Research Council (Project grant), grant 2018-04237_VR. Participating organisations named by the source: Stockholm University. Funded amount: SEK 3,780,000, as stated by the source. Runs 2018-12-01 to 2021-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Geometri, Geometry. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-04); national funding data, not CORDIS. Abstract given by the source: The main purpose of this project is to further the understanding of exact Lagrangian manifolds in symplectic manifolds, and understand the relations to quantum physics. We propose the following specific goals:A) Apply Waldhausens K-theory to Fukaya categories to define and calculate higher K-invariants.B) Extent the notion of generating families of exact Lagrangians to a categorified version, which we call generating gerbes and which are defined for all embeddings, and hence defines new invariants of such.C) Compare with physics. There is already well-known connections between Lagrangians, generating families, and quantum physics. However, a direct relation with the deep connection between smooth structures and generating families seems unknown (unused). So, we especially want to elaborate on this connection and also generalize to the notion of generating gerbes from part B).D) Use part A) to calculate invariants defined in part B).Parts A) and B) are related to recent new development in the field (by Mohammed Abouzaid and I) and our current/previous work can be seen as small preliminary versions of what we hope to much more generally accomplish.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: A project funded by the Swedish Research Council, running from 2018 to 2021, aims to advance the understanding of exact Lagrangian manifolds and their relations to quantum physics, with a focus on algebraic K-theory and geometry. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.