## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 Room #056 (Graduate School of Math. Sci. Bldg.) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya Tea: 16:30 - 17:00 Common Room

Next seminar

### 2018/05/22

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Doman Takata (The university of Tokyo)
An analytic index theory for infinite-dimensional manifolds and KK-theory (JAPANESE)
[ Abstract ]
The Atiyah-Singer index theorem is one of the monumental works in geometry and topology, which states the coincidence between analytic index and topological index on closed manifolds. The overall goal of my research is to formulate and prove an infinite dimensional version of this theorem. For this purpose, it is natural to begin with simple cases, and my current problem is the following: For infinite-dimensional manifolds equipped with a "proper and cocompact" action of the loop group of the circle, construct a loop group equivariant index theory, from the viewpoint of KK-theory. Although this project has not been completed, I have constructed several core objects for the analytic side of this problem, including a Hilbert space regarded as an "$L^2$-space", in arXiv:1701.06055 and arXiv:1709.06205. In this talk, I am going to report the progress so far.