Семинары: P. Piazza,

СЕМИНАРЫ


Некоммутативная геометрия и топология 9 декабря 2021 г. 16:45, г. Москва, Доклад состоится через ZOOM

[Primary and Secondary invariants of Dirac operators on G-proper manifolds] P. Piazza
Аннотация: In this talk I shall explain how cyclic cohomology and K-theory can be used in order to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group . I will first treat the case of cyclic cocycles associated to elements in the differentiable cohomology of $G$; I will then move to delocalized cyclic cocycles. I will explain the challenges in defining the delocalized eta invariant associated to the orbital integral defined by a semisimple element g in G and in showing that such an invariant enters in an Atiyah-Patodi-Singer index theorem for cocompact G-proper manifolds. I will then move to a higher version of these results, using the higher delocalized cyclic cocycles defined by Song and Tang. This talk is based on two articles with Hessel Posthuma and a recent article with Hessel Posthuma, Yanli Song and Xiang Tang. Zoom Confernece: Identifier 817 4069 6665 Password: 391118 Язык доклада: английский