16 September 2018 | 5:31 pm

We now begin the rigorous theory of the incompressible Navier-Stokes equations where is a given constant (the kinematic viscosity, or viscosity for short), is an unknown vector field (the velocity field), and is an unknown scalar field (the pressure field). Here is a time interval, usually of the form or . We will either be […]

11 September 2018 | 11:40 pm

In the last week or so there has been some discussion on the internet about a paper (initially authored by Hill and Tabachnikov) that was initially accepted for publication in the Mathematical Intelligencer, but with the editor-in-chief of that journal later deciding against publication; the paper, in significantly revised form (and now authored solely by […]

10 September 2018 | 7:31 pm

Joni Teräväinen and I have just uploaded to the arXiv our paper “The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures“. This is a sequel to our previous paper that studied logarithmic correlations of the form where were bounded multiplicative functions, were fixed shifts, was […]