FMSPレクチャーズ

過去の記録 ~03/29次回の予定今後の予定 03/30~

担当者 河野俊丈

2018年10月31日(水)

15:00-16:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (4/4)
Lecture 4. BEYOND ELLIPTICITY or K-HOMOLOGY AND INDEX THEORY ON CONTACT MANIFOLDS (ENGLISH)
[ 講演概要 ]
K-homology is the dual theory to K-theory. The BD (Baum-Douglas) isomorphism of Atiyah-Kasparov K-homology and K-cycle K-homology provides a framework within which the Atiyah-Singer index theorem can be extended to certain differential operators which are hypoelliptic but not elliptic. This talk will consider such a class of differential operators on compact contact manifolds. These operators have been studied by a number of mathematicians (e.g. C.Epstein and R.Melrose).
Operators with similar analytical properties have also been studied (e.g. by Alain Connes and Henri Moscovici --- also Michel Hilsum and Georges Skandalis). Working within the BD framework, the index problem will be solved for these differential operators on compact contact manifolds.
This is joint work with Erik van Erp.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf