Collapsing is a generic term indicating

degeneration of manifolds under limits.

A very simple example is that of a bundle

collapsing to the basis via shrinking of the metric on the fibers.

In the first part of this talk I will detail limiting behaviors

of eigenvalues of the Orbifold Laplacian, while

in  the second part I will detail a noncommutative

geometry framework for collapsing of  Dirac operator eigenvalues.

References:

C. Farsi, E. Proctor, and C. Seaton, Gamma-extensions of the

spectrum of an orbifold Trans. Amer. Math. Soc. 366 (2014),

3881–3905.

C. Farsi, E. Proctor, and C. Seaton, Approximating orbifold

spectra using collapsing connected sums, J. Geom. Anal. 31

(2021), 9433–9468.

C. Farsi anf F. Latrémolière, Collapse in Noncommutative

Geometry and Spectral Continuity, Accepted by the Journal of

the London Mathematical Society, to appear.