Appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

I will present a new tool for the calculation of motivic invariants appearing in Donaldson-Thomas theory, such as the motivic Milnor fiber and motivic nearby fiber, starting from a theory of volumes of semi-algebraic sets introduced a decade ago by Hrushovski and Kazhdan. The key new result for applications is a tropical Fubini theorem; the invariants of interest can be computed by integrating the volumes of fibers of the tropicalization map with respect to Euler characteristic on the base. This is joint work with Johannes Nicaise.