# Anda Degeratu : An analytical approach towards understanding the topology of crepant resolutions of Calabi-Yau orbifolds

A Calabi-Yau orbifold in complex dimension 3 is locally modeled on C^3/G where G is a finite subgroup of SL(3,C). From a geometrical perspective I view this as an orbifold with boundary S^5/G. To the geometry of the boundary we can associate the $\eta$-invariant which measures the spectral asymmetry of the Dirac operator. It turns out that this analytical invariant is already encoded in the algebraic package describing the variety C^3/G. In the first part of my talk I will describe this very curious relation. In the second part, I will focus on the case of isolated singularities and their crepant resolutions. Via the Atiyah-Patodi-Singer index theorem, the $\eta$-invariant is used to gain information about multiplicative structure in cohomology. This is expressed in terms of the representation theory of the finite group.

**Category**: String Theory**Duration**: 56:51**Date**: February 8, 2001 at 4:00 PM**Views**: 24-
**Tags:**seminar, String Theory Seminar

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