Refereed research papers

  1. RR-BS correspondence --a localization phenomenon of index in Geometric quantization-- , Sugaku 71 (2019), no. 1, 1-30. (Japanese)

  2. With H. Fujita and M. Furuta, Torus fibrations and localization of index III, Comm. Math. Phys. 327 (2014), isuue 3, 665-689.

  3. With H. Fujita and M. Furuta, Torus fibrations and localization of index II, Comm. Math. Phys. 326 (2014), issue 3, 585-633.

  4. Equivariant local index, RIMS Kôkyûroku Bessatsu B39 (2013), 215-232.

  5. Local torus actions modeled on the standard representation, Adv. Math. 227 (2011), no. 5, 1914-1955.

  6. With H. Fujita and M. Furuta, Torus fibrations and localization of index I, J. Math. Sci. Univ. Tokyo 17 (2010), no. 1, 1-26.

  7. On manifolds which are locally modeled on the standard representation of a torus, Noncommutativity and Singularities, 353-363. Advanced Studies in Pure Mathematics 55. Mathematical Society of Japan, Tokyo, 2009.

  8. On liftings of local torus actions to fiber bundles, Toric Topology, 391-402. Contemp. Math. 460. American Mathematical Society, Providence, RI, 2008.

  9. On the geometric quantization of the moduli space of flat connections on a punctured Riemann surface , Review Bull. Cal. Math. Soc. 12 (2004), no. 1-2, 97-108.

  10. With Y. Kamiyama, Symplectic toric space associated to triangle inequalities, Geometriae Dedicata 93 (2002), no.1, 25-36.

  11. The Generating function for certain cohomology intersection pairings of the moduli space of flat connections, J. Math. Sci. Univ. Tokyo 8 (2001), no. 3, 541-558.

Thesis

  1. Quantization of the moduli space of flat connections on a punctured Riemann surface based on symplectic geometry, Ph.D thesis, Graduate school of Mathematical Sciences, The University of Tokyo (2003).

Proceedings

  1. Equivariant local index and symplectic cut, New transformation groups and its related topics, to appear in RIMS K\^oky\^uroku , Kyoto, 2016. PDF .

  2. RR=#BS via localization of index, Trends in Mathematics 12 (2010), no. 1, 1-41. PDF .

  3. On the existence of symplectic structures compatible with local torus actions, Proccedings of 34th Symposium on Transformation Groups, 91-96. Wing Co.,Ltd, Wakayama, 2007. PDF .

  4. On Local torus actions modeled on the standard representation, The theory of transformation groups and its applications, 94-106. RIMS Kôkyûroku 1569, Kyoto, 2007. PDF .

  5. Locally standard torus fibrations, Proccedings of 33th Symposium on Transformation Groups, 107-118, Wing Co., Ltd, Wakayama, 2007. PDF .

  6. Twisted toric structures, The 2nd COE Conference for Young Researchers, 233-238. Hokkaido University Technical Report Series in Mathematics 104, Hokkaido, 2006. PDF .

Preprints

  1. Adiabatic limits, Theta functions, and Geometric quantization, 41 pages. PDF . Also available at arXiv:1904.04076.

  2. A formula for the equivariant local index of the reduced space in the symplectic cutting, MIMS Technical Report No. 00044, 2014. 7 pages. Also available at arXiv:1402.6437.

  3. With H. Fujita and M. Furuta, Geodesic flows on spheres and the local Riemann-Roch numbers, UTMS Preprint Series 2012-12. 12 pages. Also available at arXiv:1209.2924.

  4. Equivariant local index, MIMS Technical Report No. 00037, 2011. 13 pages.

  5. With H. Fujita and M. Furuta, Torus fibrations and localization of index III, UTMS Preprint Series 2010-11. 25 pages. (old version)

  6. RR=#BS via localization of index, MIMS Technical Report No. 00029, 2010. 41 pages.

  7. With H. Fujita and M. Furuta, Torus fibrations and localization of index II, UTMS Preprint Series 2009-21. 50 pages. (old version)

  8. WITH H. Fujita and M. Furuta, Acyclic Polarizations and localization of Riemann-Roch numbers I, UTMS Preprint Series 2008-12. 22 pages. Old version of "Torus fibrations and localization of index I".

  9. Twisted toric structures, UTMS Preprint Series 2006-10. 40 pages. PDF .

  10. Perfect Bott-Morse function on polygon space, (2000), 11 pages. PDF .