Publications

(All pdf files will be available here, eventually. Most recent articles are available on the arXiv.)

1. Books

2. Articles

3. Miscellaneous


1. Books

Painleve III: A Case Study in the Geometry of Meromorphic Connections (with C. Hertling), Lecture Notes in Mathematics 2198, Springer, 2017 link to Springer website (xii+202 pages) (preliminary version available as arXiv:1501.04812, see below) Lecture Notes in Mathematics website

From Quantum Cohomology to Integrable Systems,
Oxford University Press, 2008 (xxix+305 pages) preprint version

Harmonic Maps, Loop Groups, and Integrable Systems,
Cambridge University Press, 1997 (xiv+194 pages) preprint version


2. Articles

Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations
with Nan-Kuo Ho, preprint (arXiv: 1802.01126)

A Lie-theoretic description of the solution space of the tt*-Toda equations
with Nan-Kuo Ho, Math. Phys. Anal. Geom., published online 2017 (arXiv:1801.10445)

Isomonodromy aspects of the tt* equations of Cecotti and Vafa III. Iwasawa factorization and asymptotics,
with A. R. Its, and C.-S. Lin, preprint (arXiv:1707.00259), preprint version

The Painleve III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles, with C. Hertling, preliminary version of Painleve III: A Case Study in the Geometry of Meromorphic Connections (see above) (arXiv:1501.04812) preprint version

Isomonodromy aspects of the tt* equations of Cecotti and Vafa II. Riemann-Hilbert problem,
with A. R. Its, and C.-S. Lin, Commun. Math. Phys. 336 (2015) 337-380 (arXiv:1312.4825) preprint version

Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data,
with A. R. Its, and C.-S. Lin, Int. Math. Res. Notices 2015 11745-11784 (arXiv:1209.2045) preprint version

Some tt* structures and their integral Stokes data,
with C.-S. Lin, Commun. Number Theory Phys. 6 (2012) 785-803 (arXiv:1209.2318) preprint version

Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa,
with C.-S. Lin, J. reine angew. Math. 689 (2014) 1-32 (arXiv:1010.1889) preprint version

Differential equations aspects of quantum cohomology,
in: Geometric and Topological Methods for Quantum Field Theory, Cambridge Univ. Press, 2010, 54-85 (arXiv:0906.0641) preprint version

The tt* structure of the quantum cohomology of C P^1 from the viewpoint of differential geometry,
with J. Dorfmeister and W. Rossman, Asian J. Math 14 (2010) 417-438 (arXiv:0905.3876) preprint version

Orbifold quantum D-modules associated to weighted projective spaces,
with H. Sakai, Comm. Math. Helv. 89 (2014) 273-297 (arXiv:0810.4236) preprint version

Gromov-Witten invariants of flag manifolds, via D-modules,
with A. Amarzaya,
Jour. London Math. Soc. 72 (2005) 121-136 (arXiv:math/0306372) preprint version

Quantum cohomology via D-modules,
Topology 44 (2005) 263-281 (arXiv:math/0206212) preprint version

Introduction to homological geometry: I,
in: Integrable Systems, Geometry, and Topology,
AMS/IP Studies in Advanced Mathematics 36, 2006, 123-150 (arXiv:math/0104274) preprint version

Introduction to homological geometry: II,
in: Integrable Systems, Geometry, and Topology,
AMS/IP Studies in Advanced Mathematics 36, 2006, 83-121(arXiv:math/0105032) preprint version

An update on harmonic maps of finite uniton number via the zero curvature equations,
in: Integrable Systems, Topology, and Physics, Contemporary Mathematics 309, American Mathematical Society, 2002,
85-113 (arXiv:math/0105110) preprint version

Morse Theory in the 1990's,
in: Invitations to Geometry and Topology, Oxford University Press, 2002, 146-207 (arXiv:math/0104155) preprint version

Quantum cohomology and the periodic Toda lattice,
with T. Otofuji,
Commun. Math. Phys. 217 (2001) 475-487 (arXiv:math/9812127) preprint version

Pseudo vector bundles and quasifibrations,
with M. Kwiecinski and A. Ong,
Hokkaido J. Math. 29 (2000) 159-170 (arXiv:math/9807103) preprint version

Spaces of polynomials with roots of bounded multiplicity,
with A. Kozlowski and K. Yamaguchi,
Fundamenta Math. 161 (1999) 93-117 (arXiv:math/9807053) preprint version

Stable splitting of the space of polynomials with roots of bounded multiplicity,
with A. Kozlowski and K. Yamaguchi,
Jour. Math. Kyoto Univ. 38 (1998), 351-366 preprint version

Actions of loop groups, deformations of harmonic maps, and their applications,
with Y. Ohnita,
in: Selected Papers on Harmonic Analysis, Groups and Invariants,
Amer. Math. Soc. Translations 183, 1998, 33-50 PDF UNAVAILABLE AT THIS TIME

Harmonic two-spheres in compact symmetric spaces, re-visited,
with F. E. Burstall,
Math. Annalen 309 (1997), 541-572 (arXiv:dg-ga/9606002) preprint version

Homological stability of oriented configuration spaces,
with A. Kozlowski and K. Yamaguchi,
Jour. Math. Kyoto Univ. 36 (1996), 809-814 PDF UNAVAILABLE AT THIS TIME

Integrable Systems, Loop Groups, and Harmonic Maps,
Seminar in Math. Sciences 22, Keio University, 1995 PDF UNAVAILABLE AT THIS TIME

The homotopy type of the space of rational functions,
with A. Kozlowski, M. Murayama, and K. Yamaguchi,
Jour. Math. Kyoto Univ. 35 (1995), 631-638 preprint version

The topology of the space of rational curves on a toric variety,
Acta Math. 174 (1995), 119-145 (arXiv:alg-geom/9301005) preprint version

Configuration spaces and the space of rational curves on a toric variety,
Bull. Amer. Math. Soc. 31 (1994), 191-196 (arXiv:math/9410219) preprint version

The topology of spaces of coprime polynomials,
with A. Kozlowski and K. Yamaguchi,
Math. Zeit. 217 (1994), 435-446 PDF UNAVAILABLE AT THIS TIME

Detecting exotic structures via the Thom-Pontrjagin construction,
with E. Micha,
Mathematika 41 (1994), 145-148 preprint version

Loop group actions on harmonic maps, and their applications,
with Y. Ohnita,
in: Harmonic Maps and Integrable Systems, Vieweg 1994, 273-292 preprint version

On the fundamental group of the space of harmonic 2-spheres in the n-sphere,
with M. Furuta, M. Kotani, and Y. Ohnita,
Math. Zeit. 215 (1994), 503-518 (arXiv:hep-th/9303036) preprint version

On the space of holomorphic maps from the Riemann sphere to the quadric cone,
Quarterly Jour. of Math. 45 (1994), 57-75 preprint version

Group actions and deformations for harmonic maps,
with Y. Ohnita,
Jour. Math. Soc. Japan 45 (1993), 671-704 (arXiv:hep-th/9303037) preprint version

Instantons, rational maps, and harmonic maps,
Matematica Contemporanea 2 (1992), 113-155 preprint version

Harmonic two spheres in complex projective space, and some open problems,
Expo. Math. 10 (1992) 61-87 preprint version

Actions of loop groups on harmonic maps,
with M. Bergvelt,
Trans. Amer. Math. Soc. 326 (1991), 861-886 preprint version

The energy function and homogeneous harmonic maps,
Proc. Lond. Math. Soc. 62 (1991) 77-98 preprint version

Holomorphic curves in loop groups,
with A. N. Pressley,
Commun. Math. Phys. 118 (1988) 511-527 Project Euclid open access

Lie groups as framed boundaries,
with L. Astey and G. Pastor,
Osaka Jour. Math. 25 (1988) 891-907 Project Euclid open accesss

The energy of harmonic maps obtained by the twistor construction,
in: Harmonic Mappings, Twistors, and Sigma Models, World Scientific 1988, 178--202 PDF UNAVAILABLE AT THIS TIME

Geometry of maps between generalized flag manifolds,
Jour. Diff. Geom. 25 (1987) 223-247 PDF UNAVAILABLE AT THIS TIME

Orbits and harmonic maps,
in: The Lefschetz Centennial Conference III: Proceedings in Differential Equations, Contemp. Math. 58 III (1987) 161-171 PDF UNAVAILABLE AT THIS TIME

Instantons and harmonic maps,
in: Infinite Dimensional Groups with Applications, MSRI Publ. 4, Springer 1985, 137-156 PDF UNAVAILABLE AT THIS TIME

Geodesics, harmonic maps, and the Yang-Mills equations,
in: Topics in Several Complex Variables, Res. Notes in Math. 112, Pitman 1985, 102-108 PDF UNAVAILABLE AT THIS TIME

Topology of the space of absolute minima of the energy functional,
Amer. Jour. Math. 106 (1984) 21-42 PDF UNAVAILABLE AT THIS TIME

Variedades que tienen a un grupo de Lie como frontera, y teoria de representaciones,
Sem. Esp. de Topologia 6 (1983), 55-71 PDF UNAVAILABLE AT THIS TIME

Morse-Bott decompositions and framings of compact Lie groups,
Sem. Esp. de Topologia 4 (1982), 13-25 PDF UNAVAILABLE AT THIS TIME


3. Miscellaneous

Introduction to manifolds (lecture notes from a course at Keio University)

An introduction to global analysis and the calculus of variations (lecture notes from a course at the University of Rochester) (pre-TeX era)

A brief introduction to LaTeX (step by step TeX files from a "research literacy" course at Tokyo Metropolitan University)

slides from colloquium talk at Waseda University 2015/5/28 早稲田大学での談話会