Hiroshige Kajiura -- research
On my research
update:
May 31, 2014,
Research interest
under construction
-
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
- ...
Key words:
Algebraic topology (operads, homotopy algebras, ...);
Deformation quantization and Noncommutative geometry;
Homological or categorical algebra;
String theory and quantum field theory
(topological strings, mirror symmetry
and homological mirror symmetry, BV-formalism, string field theory, ...);
Algebraic geometry related to singularities,
Lagrangians in symplectic geometry,
Representation theory of quivers ....
Expository article
- "On A-infinity enhancements for triangulated categories," (in Japanese)
[pdf] May 22, 2014.
- ...
- ``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.
- ``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)
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 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))
Book
-
SGC 75
"Category theory for mathematical physics," (in Japanese), July 2010
webpage for corrections
-
Lectures in Mathematical Sciences, The University of Tokyo,
``Introduction to deformation quantization,'' (in Japanese)
with Y. Maeda (note: by R. Takamura), May 2002
Table of the content
[dvi]
[pdf]
[ps]