On my research

update: July 8, 2007,

Research interest

• Algebraic structures (operads, homotopy algebras, ...) associated to compactifications of moduli spaces of punctured Riemann surfaces
• Algebraic structures associated to various geometry as representations over those operads, etc.,
• Deformation of geometry as deformation of those algebraic structures
• ...

Some of recent preprints

• ``An $A_\infty$-structure for lines in a plane,'' [arXiv: math.QA/0703164] Acknowlegement
  
• ``Homotopy algebra of open-closed strings,''
  with Jim Stasheff, to appear in Proceedings of the conference "Groups, Homotopy and Configuration Spaces -- in honor of Fred Cohen" held in July, 2005 at Univ. of Tokyo, [arXiv:hep-th/0606283]
• ``Matrix factorizations and representations of quivers II: type ADE case,''
  with Kyoji Saito and Atsushi Takahashi, [arXiv:math.ag/0511155]
• ``Star product formula of theta functions,''
  [arXiv:math.qa/0510307]
  revised version [ps], [pdf], November 8, 2005.
• ``Categories of holomorphic line bundles on higher dimensional noncommutative complex tori,''
  [arXiv:hep-th/0510119]
• ``Open-closed homotopy algebra in mathematical physics,''
  with Jim Stasheff, [arXiv:hep-th/0510118]
• ``Homotopy algebra inspired by open-closed string field theories,''
  with Jim Stasheff, [arXiv:math.qa/0410291]
• ``Homological mirror symmetry on noncommutative two-tori,''
  [arXiv:hep-th/0406233]
• ``Noncommutative homotopy algebras associated with open strings,''
  Based on doctoral thesis, Graduate School of Mathematical Sciences, Univ. of Tokyo; [arXiv:math.qa/0306332]
  

Transparencies

• ``Homological perturbation theory and Homological mirror symmetry: the $\R^2$ case,'' [ps] [pdf]
  (Talk given at ``Higher Structures in Geometry and Physics; in honor of Jim Stasheff's 70 birthday and Murray Gerstenhaber's 80's birthday'' at Henri Poincare Institute, Paris, France, January 18, 2007,
  related to the talk given at ``L-S category and $A_\infty$-structure'' at Karatsu-city hole, November 1, 2006.
  This presents the background of the paper ``An $A_\infty$-structure for lines in a plane,''
  
• ``On algebraic models for Morse homotopy and their noncommutative deformations,'' (in Japanese) [ps] [pdf]
  (Proceeding of the talk given at 53th geometry symposium, Kanazawa university, August 6, 2006, with a few corrections.
• ``On homotopy algebras and their applications to string theory,'' [pdf] [ps]
  (Talk given at Homotopy theory conference 2005, March 19-21 at Nagoya Institute of Technology; some of what were explained on the blackboard is added (April 28, 2005))

Expository article

• ``String theory and deformation quantization,'' Yoshiaki Maeda, Hiroshige Kajiura
  
• ``Deformation theory, homotopy algebras and string theory,'' (in Japanese) [pdf]
  A rough draft for a talk on a deformation theory aspect of open-closed homotopy algebras (OCHAs)

Book

• Lectures in Mathematical Sciences, The University of Tokyo (japanese only),
  ``Introduction to deformation quantization,'' (in Japanese) with Y. Maeda (note: by R. Takamura), May 2002
  Table of the content [dvi] [pdf] [ps]