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微分幾何・トポロジーセミナー

タイトル	Theory of local index and its applications
開催日時	2015年12月21日 17:00-18:30　(開始時間がいつもと異なります。)
主催者
講演者	吉田　尚彦　氏　(明治大学)
場所	14-733（14棟7階ミーティング3）
内容	We report a recent progress of the joint work with H. Fujita and M. Furuta on an index theory of a Dirac-type operators on possibly non-compact Riemannian manifolds. In our work we make use of a structure oftorus fibration on the end, and perturb a Dirac-type operator in terms offirst order differential operators along fibers on the end which satisfy a kind of acyclic condition. The perturbation allows an interpretation as an adiabatic limit or an infinite dimensional analogue of the Witten deformation. We also explain applications to the geometric quantization of Lagrangian fibrations, the quantization conjecture by Guillemin-Sternberg that implies the quantization commutes with the reduction, and the Danilov formula for the equivariant Riemann-Roch indices of the toric varieties.
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