The famous Atiyah-Singer index theorem announced in 1963 computed the index of the elliptic operator, which is defined analytically, in a topological way. In 1968, Atiyah and Segal established a localization formula for the equivariant index which computes the equivariant index via the contribution of the fixed point sets of the group action. It is natural to ask if the localization property holds for the more complex spectral invariants, e.g., eta-invariant.
The eta-invariant was introduced in the 1970's as the boundary contribution of index theorem for compact manifolds with boundary. It is formally equal to the number of positive eigenvalues of the Dirac operator minus the number of its negative eigenvalues and has many applications in geometry, topology, number theory and theoretical physics. It is not computable in a local way and not a topological invariant.
In this talk, we will establish a version of localization formula for equivariant eta-invariants by using differential K-theory, a new research field in this century.
会议网址：https://meeting.tencent.com/s/hOAu27vuKXuO
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刘博，华东师范大学紫江青年学者。2007年本科毕业于中国科学技术大学数学系，2013年在南开大学陈省身数学研究所获得博士学位，师从张伟平院士；2014年到2016年，先后在德国科隆大学与德国柏林洪堡大学从事博士后研究。2017年入职华东师范大学。主要研究方向为流形上的整体分析，Atiyah-Singer 指标理论与微分K理论。 其研究成果发表在Invent. Math.、Trans. Amer. Math. Soc.、Math. Z. 等国际期刊上。
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