The Farrell-Jones Conjecture for normally poly-free groups
Brück, B
Kielak, D
Wu, X
(04 Jun 2019)
doi:10.48550/arxiv.1906.01360
Non-crossing partitions
Baumeister, B
Bux, K
Götze, F
Kielak, D
Krause, H
(04 Mar 2019)
doi:10.48550/arxiv.1903.01146
The agrarian polytope of two-generator one-relator groups
Henneke, F
Kielak, D
(10 Dec 2019)
doi:10.48550/arxiv.1912.04650
$\ell^2$ Betti numbers and coherence of random groups
Kielak, D
Kropholler, R
Wilkes, G
(13 Mar 2020)
doi:10.48550/arxiv.2003.06354
Isoperimetric inequalities for Poincaré duality groups
Kielak, D
Kropholler, P
(18 Aug 2020)
doi:10.48550/arxiv.2008.07812
JSJ decompositions and polytopes for two-generator one-relator groups
Gardam, G
Kielak, D
Logan, A
(21 Oct 2025)
doi:10.48550/arxiv.2101.02193
Agrarian and $\ell^2$-Betti numbers of locally indicable groups, with a twist
Kielak, D
Sun, B
(14 Dec 2021)
doi:10.48550/arxiv.2112.07394
The Surface Group Conjectures for groups with two generators
Gardam, G
Kielak, D
Logan, A
(22 Feb 2022)
doi:10.48550/arxiv.2202.11093
Group rings of three-manifold groups
Kielak, D
Linton, M
(28 Mar 2023)
doi:10.48550/arxiv.2303.15907
Fri, 08 May 2026
16:00 -
17:00
L1
On Hilbert’s sixth problem: from particles to waves
Prof. Zaher Hani
(University of Michigan)
Abstract
In his sixth problem, Hilbert called for the derivation of the equations of fluid mechanics—such as the Euler and Navier-Stokes equations—from first principles, by rigorously justifying Boltzmann’s kinetic theory. This entails starting from Newton’s laws for a system of N particles and taking successive limits to first obtain Boltzmann’s kinetic equation, and then deriving the equations of fluid mechanics from it. The major landmark in the early literature is the work of Oscar Lanford (1975), who provided the first rigorous derivation of the Boltzmann equation, albeit only for short times. Hilbert’s sixth problem, however, requires a long-time version of Lanford’s result, which remained open for decades.
In a joint work with Yu Deng (University of Chicago) and Xiao Ma (University of Michigan), we extended Lanford’s theorem to long times—specifically, for as long as the solution of the Boltzmann equation exists. This allowed us to fully carry out Hilbert’s program and derive the fluid equations in the Boltzmann–Grad limit. The underlying strategy builds on earlier joint work with Yu Deng that resolved a parallel problem in which colliding particles are replaced by nonlinear waves, thereby establishing the mathematical foundations of wave turbulence theory. In this talk, we will review this progress and discuss some related problems and future directions.