# A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory

## TL;DR

This paper introduces a tropical motivic Fubini theorem that advances the calculation of motivic nearby fibers and Milnor fibers, providing new proofs and confirming conjectures in motivic Donaldson-Thomas theory.

## Contribution

It develops a novel motivic Fubini theorem for tropicalization, enabling new proofs of key conjectures in motivic Donaldson-Thomas theory.

## Key findings

- Proved a conjecture of Davison and Meinhardt on motivic nearby fibers.
- Provided a new, concise proof of the integral identity conjecture of Kontsevich and Soibelman.
- Enhanced computational tools for motivic invariants using tropical geometry.

## Abstract

We present a new tool for the calculation of Denef and Loeser's motivic nearby fiber and motivic Milnor fiber: a motivic Fubini theorem for the tropicalization map, based on Hrushovski and Kazhdan's theory of motivic volumes of semi-algebraic sets. As applications, we prove a conjecture of Davison and Meinhardt on motivic nearby fibers of weighted homogeneous polynomials, and give a very short and conceptual new proof of the integral identity conjecture of Kontsevich and Soibelman, first proved by L\^e Quy Thuong. Both of these conjectures emerged in the context of motivic Donaldson-Thomas theory.