The spectrum of the Laplace-Beltrami operator acting on functions on a hyperbolic manifold tells us a great deal about its underlying geometric and topological properties. However, from the point of view of representation theory, this is just a portion of the full right regular representation, namely they are all spherical representations. In this talk, we discuss the non-spherical representations for (spin) hyperbolic surfaces (eg.: spinors) and hyperbolic 3-manifolds (eg.: 1-forms) and construct examples with uniform spectral gaps and discuss some applications. Based on joint works with Amina Abdurrahman, Anshul Adve, Ben Lowe and Jonathan Zung.
Zoom Meeting: https://icts-res-in.zoom.us/j/93627770536?pwd=KFQ6gsGTA9ykMbGmgZLbaVTI0QcBoV.1
Meeting ID: 936 2777 0536
Passcode: 368663