The Behrend function, introduced by Behrend, is a fundamental object in Donaldson-Thomas theory for Calami-Yau threefolds. The original topological Euler characteristic of the Donaldson-Thomas moduli space is modified by the Behrend function which is now called the weighted Euler characteristic. This is the same as the Donaldson-Thomas invariant defined by R. Thomas using the techniques of virtual fundamental class. In this talk I will talk about the notion of Behrend function and its relation to the recent consection localization techniques of Kiem-Li.

I will also talk about the motivic version of the Behrend function in order to categorify Donaldson-Thomas invariants. The motivic version of the Joyce-Song formulas for the Behrend function identities are essential to the wall crossing of the motivic Donaldson-Thomas invariants and I will outline the proof ofsuch formulas. Speaker(s): Yunfeng Jiang (University of Kansas)