241 citations · 1.1k across the 41 of their papers we have counts for
45 papers
Notes on the decomposition theorem for blowups
Hiroshi Iritani
We discuss arithmetic and Hodge-theoretic properties of the isomorphisms appearing in the decomposition theorem for quantum cohomology of blowups. These properties underpin the app…
Fourier analysis of equivariant quantum cohomology
Hiroshi Iritani
Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests th…
Revisiting Gamma conjecture I: counterexamples and modifications
Sergey Galkin, Jianxun Hu, Hiroshi Iritani +3
We continue investigation of asymptotics of quantum differential equation for Fano manifolds, with a special regard to Gamma conjecture I and its underlying Conjecture $\mathcal{O}…
Gamma conjecture and tropical geometry
Hiroshi Iritani
Hodge-theoretic mirror symmetry for a Calabi-Yau mirror pair says that the variation of Hodge structure arising from quantum cohomology of a Calabi-Yau manifold and that arising fr…
Gamma classes and quantum cohomology
Hiroshi Iritani
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 inte…
Quantum D-modules of toric varieties and oscillatory integrals
Hiroshi Iritani
We review mirror symmetry for the quantum cohomology D-module of a compact weak-Fano toric manifold. We also discuss the relationship to the GKZ system, the Stanley-Reisner ring, t…