#### Alladi Ramakrishnan Hall

#### APS η-invariant, path integrals, and mock modularity

#### Diksha Jain

##### University of Sissa

*I will show that the Atiyah-Patodi-Singer η-invariant can be related to the temperature-dependent Witten index of a noncompact theory and will give a new proof of the APS theorem using scattering theory. I will then motivate how the η-invariant can be computed using path integral and use this method to compute η-invariant for Cigar. The relation between η-invariant and Mock modular forms will also be hinted.*

Done