Mathematics Colloquium

I will present a new tool for the calculation of motivic invariants appearing in Donaldson-Thomas theory, such as the motivic Milnor fiber, starting from a theory of volumes of semi-algebraic sets introduced a decade ago by Hrushovski and Kazhdan. They 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.