Gamma classes and quantum cohomology

Author:

Hiroshi Iritani

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), High Energy Physics - Theory (hep-th), Symplectic Geometry (math.SG)

journal:

date:

2023-07-28 16:00:00

Abstract

The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum connection. We present several conjectures (the Gamma-conjectures) about this structure, particularly focusing on the Riemann-Hilbert problem it poses. We also discuss a conjectural functoriality of quantum cohomology under birational transformations.

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