The Surface Group Conjectures for groups with two generators
 Gardam, G Kielak, D Logan, A (22 Feb 2022)
Group rings of three-manifold groups
 Kielak, D Linton, M (28 Mar 2023)
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. 

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Kira Patel wins EPSRC Best Poster prize

We'd like to say a big congratulations to Kira Patel, now a 4th year mathematics undergraduate, who won the prize for the best Engineering and Physical Sciences Research Council (EPSRC) Vacation Internships poster at the EPSRC Poster Event on November 6th. Kira's poster title was 'A viscous catenary in glass tube manufacture'. She was supervised by Prof. Peter Howell.

Song of the Week: Roy Wood - Forever

You know those songs from your early childhood that you liked at the time, but suspect were probably a bit rubbish. So after years of silence you nervously play them again and..

Turns out they were actually a bit fab. This video is from a Dutch tv show.

Roy Wood is best known for Wizard's I Wish it Could be Christmas Everyday, as well as being a member of the Move and ELO - and for being very underrated (it turns out).

Disability History Month

Disability History Month is marked from 20th November to 20th December, which gives us an opportunity to raise awareness of disability and support available in the University. 

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