Program
- 組織委員：
- 新井仁之（東大），儀我美一（東大／北大）
- 幹事：
- 石井仁司（早大），河添 健（慶大），剣持信幸（千葉大），酒井 良（都立大），柴田良弘（早大），望月 清（中央大），宮地晶彦（東女大），山崎昌男（早大），山本昌宏（東大）
- 日 時：
- 2006年10月30日(月) 16:30-17:30
- 場 所：
- 東京大学大学院 数理科学研究科128号室
※会場へのアクセスは下記にてご確認下さい。
駒場アクセスマップ
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
駒場キャンパス数理科学研究科棟
http://www.u-tokyo.ac.jp/campusmap/cam02_01_27_j.html
- 講 演 者：
- Matti Lassas (Helsinki University of Technology, Institute of Mathematics)
- 演 題：
- Inverse Problems and Index Formulae for Dirac Operators
- ABSTRACT:
We consider a selfadjoin Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M, g)$ with a nonempty boundary.
The operator $D_P$ is specified by a boundary condition $P(u|_{\partial M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator. We assume the existence of a chirality operator which decomposes $L2(M, V)$ into two orthogonal subspaces $X_+ \oplus X_-$.
In the talk we consider the reconstruction of $(M, g)$, $V$, and $D_P$ from the boundary data on $\partial M$.
The data used is either the Cauchy data, i.e. the restrictions to $\partial M \times R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\times \C4$, $M \subset \R3$. The presented results have been done in collaboration with Yaroslav Kurylev (Loughborough, UK).
