Hiroshi Iritani

J-GLOBAL         Last updated: Oct 12, 2019 at 16:49
Hiroshi Iritani
Kyoto University
Graduate School of Science Division of Mathematics

Research Areas


Academic & Professional Experience

Apr 2018
Professor, Kyoto University
Apr 2010
Mar 2018
Assoicate Professor, Kyoto University
Apr 2007
Mar 2010
Assistant Professor, Kyushu University
Oct 2006
Mar 2007
Assistant Professor, Kyushu University

Awards & Honors

Spring Prize
Geometry Prize

Published Papers

Coates Tom, Iritani Hiroshi
KYOTO JOURNAL OF MATHEMATICS   58(4) 695-864   Dec 2018   [Refereed]
Coates Tom, Iritani Hiroshi, Jiang Yunfeng
ADVANCES IN MATHEMATICS   329 1002-1087   Apr 2018   [Refereed]
Hiroshi Iritani
Mathematische Annalen   368(1) 279-316   Jun 2017   [Refereed]
© 2016 Springer-Verlag Berlin HeidelbergWe identify a certain universal Landau–Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the primitive for...
Hiroshi Iritani
Geometry and Topolgy   21(1) 315-343   2017   [Refereed]
Hiroshi Iritani, Jifu Xiao
Kyoto J. Math.   56(4) 873-905   Dec 2016   [Refereed]
Sergey Galkin, Vasily Golyshev, Hiroshi Iritani
Duke Mathematical Journal   165(11) 2005-2077   Jan 2016   [Refereed]
© 2016.We propose Gamma conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class...
Hiroshi Iritani, Etienne Mann, Thierry Mignon
International Mathematics Research Notices   2016(9) 2828-2888   Jan 2016   [Refereed]
© 2015 The Author(s). Published by Oxford University Press. All rights reserved.We give an interpretation of quantum Serre theorem of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit...
Iritani Hiroshi
SUGAKU   68(4) 337-360   2016   [Refereed][Invited]
Glasgow Mathematical Journal   58(3) 717-726   Jul 2015   [Refereed]
Copyright © Glasgow Mathematical Journal Trust 2015Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, t...
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian Hua Tseng
Compositio Mathematica   151(10) 1878-1912   Jan 2015   [Refereed]
© The Authors 2015.We prove a Givental-style mirror theorem for toric Deligne-Mumford stacks χ. This determines the genus-zero Gromov-Witten invariants of χ in terms of an explicit hypergeometric function, called the I-function, that takes values ...
Tom Coates, Hiroshi Iritani
Michigan Mathematical Journal   64(3) 587-631   Jan 2015   [Refereed]
Let X be a smooth projective variety. The Gromov-Witten potentials of X are generating functions for the Gromov-Witten invariants of X: they are formal power series, sometimes in infinitely many variables, with Taylor coefficients given by Gromov-...
Hiroshi Iritani, Todor Milanov, Valentin Tonita
International Mathematics Research Notices   2015(11) 2887-2937   Jan 2015   [Refereed]
© The Author(s) 2014. Published by Oxford University Press. All rights reserved.We give a new reconstruction method of big quantum K-ring based on the q-difference module structure in quantum K-theory [12, 13]. The q-difference structure yields co...
Tom Coates, Hiroshi Iritani, Yunfeng Jiang, Ed Segal
Pure and Applied Mathematics Quarterly   11(2) 239-266   Jan 2015   [Refereed]
© 2015, International Press of Boston, Inc. All rights reserved.We prove the following results for toric Deligne– Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant K-theory; the equivariant Hirzebruch–Ri...
Iritani Hiroshi
RIMS Kokyuroku   1918 71-87   Sep 2014
A. Chiodo; H. Iritani; Y. Ruan
Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques   119(1) 127-216   Jun 2014   [Refereed]
Eduardo Gonzalez, Hiroshi Iritani
Tohoku Math. J. (2), Volume 69, Number 3 (2017), 327-368      Jan 2013
Let M be a symplectic manifold equipped with a Hamiltonian circle action and
let L be an invariant Lagrangian submanifold of M. We study the problem of
counting holomorphic disc sections of the trivial M-bundle over a disc with
boundary in L throu...
E. González; H. Iritani
Selecta Mathematica, New Series   18(3) 557-590   Sep 2012   [Refereed]
T. Coates; A. Gholampour; H. Iritani; Y. Jiang; P. Johnson; C. Manolache
Mathematical Research Letters   19(5) 997-1005   2012   [Refereed]
Hiroshi Iritani
Ann. Inst. Fourier (Grenoble)   61(7) 2909-2958   2011   [Refereed][Invited]
In a previous paper, the author introduced an integral structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle ...
Hiroshi Iritani
Adv. Stud. Pure. Math. 59, (2010), pp.111-166   59 111-166   2010   [Refereed][Invited]
This is an expository article on the recent studies of Ruan's crepant
resolution/flop conjecture and its possible relations to the K-theory integral
structure in quantum cohomology.
H. Iritani
Advances in Mathematics   222(3) 1016-1079   Oct 2009   [Refereed]
T. Coates; A. Corti; H. Iritani; H.-H. Tseng
Duke Mathematical Journal   147(3) 377-438   Apr 2009   [Refereed]
T. Coates; H. Iritani; H.-H. Tseng
Geometry and Topology   13(5) 2675-2744   2009   [Refereed]
H. Iritani
Topology   47(4) 225-276   Sep 2008   [Refereed]
H. Iritani
Journal fur die Reine und Angewandte Mathematik   610(610) 29-69   Sep 2007   [Refereed]
H. Iritani
Mathematische Zeitschrift   252(3) 577-622   2006   [Refereed]
Journal of Computer Chemistry, Japan   5(2) 65-80   Jun 1999   [Refereed]
The number of structural isomers of alkanes was combinatorially enumerated by counting the different structures composed of several alkyl groups attached to the center of the molecule specifically defined. This algorithm is rather slow when compar...


Hiroshi Iritani
   Jun 2019
We introduce a global Landau-Ginzburg model which is mirror to several toric
Deligne-Mumford stacks and describe the change of the Gromov-Witten theories
under discrepant transformations. We prove a formal decomposition of the
quantum cohomology D...
Mohammed Abouzaid, Sheel Ganatra, Hiroshi Iritani, Nick Sheridan
   Sep 2018
We propose a new method to compute asymptotics of periods using tropical
geometry, in which the Riemann zeta values appear naturally as error terms in
tropicalization. Our method suggests how the Gamma class should arise from the
Tom Coates, Hiroshi Iritani
   Apr 2018
We construct a sheaf of Fock spaces over the moduli space of elliptic curves
E_y with Gamma_1(3)-level structure, arising from geometric quantization of
H^1(E_y), and a global section of this Fock sheaf. The global section
coincides, near appropri...
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
   Jun 2016
Using the mirror theorem [CCIT15], we give a Landau-Ginzburg mirror
description for the big equivariant quantum cohomology of toric Deligne-Mumford
stacks. More precisely, we prove that the big equivariant quantum D-module of a
toric Deligne-Mumfo...
Hiroshi Iritani, Todor Milanov, Yongbin Ruan, Yefeng Shen
   May 2016
We construct a global B-model for weighted homogeneous polynomials based on
K. Saito's theory of primitive forms. Our main motivation is to give a rigorous
statement of the so called global mirror symmetry conjecture relating
Gromov-Witten invaria...
Sergey Galkin, Hiroshi Iritani
   Aug 2015
The asymptotic behaviour of solutions to the quantum differential equation of
a Fano manifold F defines a characteristic class A_F of F, called the principal
asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors
claims that...
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
   Jan 2014
We use the mirror theorem for toric Deligne-Mumford stacks, proved recently
by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero
Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a
mirror theorem for ...
Hiroshi Iritani
   Jun 2009
We study possible real structures in the space of solutions to the quantum
differential equation. We show that, under mild conditions, a real structure in
orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the
large radius ...
Hiroshi Iritani
   Dec 2007
We study real and integral structures in the space of solutions to the
quantum differential equations. First we show that, under mild conditions, any
real structure in orbifold quantum cohomology yields a pure and polarized
tt^*-geometry near the ...
Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
   Apr 2007
Let X be an orbifold with crepant resolution Y. The Crepant Resolution
Conjectures of Ruan and Bryan-Graber assert, roughly speaking, that the quantum
cohomology of X becomes isomorphic to the quantum cohomology of Y after
analytic continuation in...

Association Memberships


Research Grants & Projects

Study of the Gamma structure in Gromov-Witten theory
Project Year: Apr 2016 - Mar 2019
Global structure of mirror symmetry
Project Year: Apr 2013 - Mar 2016
Gromov-Witten theory and mirror symmetry
Project Year: Apr 2010 - Mar 2013    Investigator(s): Hiroshi Iritani
Study of quantum cohomology and mirror symmetry
Project Year: Apr 2007 - Mar 2007    Investigator(s): Hiroshi Iritani