Geometry and analytic theory of Frobenius manifolds
Boris Dubrovin
TL;DR
This paper explores the mathematical structure of Frobenius manifolds and their applications across various fields such as Gromov-Witten invariants, singularity theory, and integrable hierarchies, revealing deep interconnections.
Contribution
It provides a comprehensive analysis of Frobenius manifolds and highlights their unifying role in diverse mathematical theories.
Findings
Frobenius manifolds connect Gromov-Witten invariants with singularity theory.
They establish relationships between differential geometry and integrable systems.
The paper elucidates the structure of orbit spaces of reflection groups.
Abstract
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes remarkable relationships between these, sometimes rather distant, mathematical theories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory