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MONDAY May 31

Morning

0. Opening 9:30-9:40
1. M. Dubois-Violette (Paris, Orsey) 10:00-11:00
 "Lectures on graded differential algebras and noncommutative geometry(1)"　Abstract
2. M. Kato (Tokyo) 11:30-12:30
"Quick Introduction to D-brane"　Abstract

Afternoon

3. N. Ishibashi (KEK) 14:30-15:30
"Dp-brane and string theory"
4. A. Kato (Tokyo) 15:45-16:45
"Comments on Large N Matrix Model"　Abstract
5. H. Kawai (Kyoto) 17:00-18:00
"Space-time and matter in IIB matrix model"
 

TUESEDAY JUNE 1

Morning

1. T. Yoneya (Tokyo) 9:00-10:00
"String theory and quantum geometry (1)"
2. M. Dubois-Violette (Paris, Orsey) 10:15-11:15
"Lectures on graded differential algebras and noncommutative geometry(2)"
3. P. Severa (IHES) 11:30-12:30
"Quantum groups (1)"

Afternoon

4. O. Grandjean (Harvard) 14:30-15:30
"Characterization of Kaehler non-commutative spaces"　Abstract
5. T. Natsume (Nagoya IT) 15:45-16:45
"$C^*$-algebraic deformation quantization of symplectic manifolds" 　Abstract
4. M. Kato (Tokyo) 17:00-18:00
"World volume noncommutativity versus target space"　Abstract

WEDNESDAY JUNE 2

Morning

1. T. Yoneya (Tokyo) 9:00-10:00
"String theory and quantum geometry (2)"
2. M. Dubois-Violette (Paris, Orsey) 10:15-11:15
"Lectures on graded differential algebras and noncommutative geometry(3)"
3. K. Wojciechowski (IUPUI) 11:30-12:30
"Introduction to zeta-determinant of the Dirac operator and
elliptic boundary problem for the Dirac operator"

Afternoon

NO LECTURES

THURSDAY JUNE 3

Morning

1. T. Kimura (Boston) 9:00-10:00
"Operads and its applications (1)"
2. P. Wojciechowski (IUPUI) 10:15-11:15
"Quillen determinant and the Canonical determinant on the
Grassmanian of the boundary conditions"
3. P. Severa (IHES) 11:30-12:30
"Quantum groups(2)"

Afternoon

4. D. Sternheimer (Bourgone)14:30-15:30
"Deformation quantization at 21"
5. V. Ovsienko (Luminy) 15:45-16:45
"Conformally equivalent quantization"　Abstract
6. K. Mikami (Akita) 17:00-18:00
"Self-similarity of Poisson structures " 　Abstract

FRIDAY JUNE 4

Morning

1. T. Kimura (Boston) 9:00-10:00
"Operads and its applications (2)"
2. P. Wojciechowski (IUPUI) 10:15-11:15
"The equality of the Quillen determinant and zeta-determinant
on the Grassmannian"
3. P. Severa (IHES) 11:30-12:30
"Quantum groups (3)"

Afternoon

4. P. Lecomte (Universite Liege) 14:30-15:30
"Equivariant quantization ; the project case"　Abstract
5. H. Omori (SUT) 15:45-16:45
"Towards noncommutative geometry"

Organised by :

Hideki Omori(SUT, Japan), Yoshiaki Maeda(Keio, Japan),
Hitoshi Moriyoshi(Keio, Japan), Satoshi Watamura(Tohoku, Japan)
 

Supported by :

Mitsubishi Foundation
Keio University

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Abstract of Talk/Lecture

• M. Dubois-Violette The lectures will be divided in three parts as follows :
  I. Categories of algebras, bimodules and the generalization of (real) vector bundles + introduction.
  II. Differential calculi and connections.
  III. Some relations with physics :
  a) Quantum mechanics and noncommutative symplectic geometry.
  b) Classical Yang-Mills-Higgs fields and noncommutative differential calculus.
  c) Classical limits of noncommutative space-times.
  

• A. Kato I'm planning to talk about the topics which appeared as two preprints: ``D-brane Actions on K\"{a}hler Manifolds'' (hep-th/9708012) and ``Comments on Large $N$ Matrix Model'' (hep-th/9903233). In the first half, we discuss matrix model actions on K\"{a}hler geometry and how physical requirements (e.g. geodesic length is proportional to the mass) constrain the background geometry. In the latter half, we consider the large $N$ divergences in matrix perturbation using field theory technique.
• O. Grandjean We show how superconformal field theory leads to the notions of Riemannian, K\"ahler, and Hyperk\"ahler non-commutative spaces. As an application, we obtain the complex structure on the non-commutative 2-torus originally found by Alain Connes using different methods.
• Pierre Lecomte The space $\mathrm{D}_{\lambda,\mu}$ of differential operators on $R^m$ acting from the $\lambda$-densities into the $\mu$-densities is a representation of the canonical projective embedding of $\mathrm{sl}(m+1,R)$ in a natural way. In most of the cases, it is isomorphic to the graded module associated to the fitration by the order of differentiation. For $\lambda = \mu = 1/2$, This module is the space of functions on the cotangent bundle $T^*R^m$ that are polynomial on each fibers while the completion of $\mathrm{D}_{\lambda,\mu}$ is a Hilbert space. One gets thus a preferred projectively equivariant quantization that competes with the standard Moyal-Weyl quantization. \par The talk will present the complete classification of the $\mathrm{sl}(m+1,R)$-modules $\mathrm{D}_{\lambda,\mu}$, together with the necessary cohomological results, a special attention being paid to the case where $\lambda = \mu$ leading to equivariant quantization.
• K. Mikami We study the group of diffeomorphisms of a 3-dimensional Poisson torus which preserve the Poisson structure up to a constant multiplier, and the group of similarity ratios. \newpage \centerline{$C^*$-algebraic deformation quantization of symplectic manifolds}
• Toshikazu Natsume We introduce the notion of $C^*$-algebraic deformation quantization of symplectic manifolds and show its existence for a given closed symplectic manifold under a topological assumption.
• Valentin Ovsienko (joint work with C. Duval and P. Lecomte)} We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,g). In other words, we establish a canonical isomorphism between the spaces of polynomials on T*M and of differential operators on tensor densities over M, both viewed as modules over the Lie algebra o(p+1,q+1) where p+q=dim(M). This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.
• Mitsuhiro Kato
  • Quick Introduction to D-brane
    Abstract: Very brief introduction to D-brane and string will be given for non-experts.
  • World Volume Noncommutativity versus Target Space Noncommutativity
    Abstract: Dual nature of noncommutativity in the D-brane world volume and in the target space structure will be discussed by constructing the boundary state of D-brane in the noncommutative space.