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Asgar Jamneshan, Or Shalom, and myself have just uploaded to the arXiv our preprints “A Host–Kra ${{\bf F}^\omega_2}$-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the ${U^6({\bf F}^n_2)}$ norm” and “The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the ${U^k}$ Gowers uniformity norms on finite abelian groups of bounded torsion“. These two papers are both concerned with advancing the inverse theory for the Gowers norms and Gowers-Host-Kra seminorms; the first paper provides a counterexample in this theory (in particular disproving a conjecture of Bergelson, Ziegler and myself), and the second paper gives new positive results in the case when the underlying group is bounded torsion, or the ergodic system is totally disconnected. I discuss the two papers more below the fold.

The International Center for Mathematical Sciences in Edinburgh recently launched its “Mathematics for Humanity” initiative with a call for research activity proposals (ranging from small collaborations to courses, workshops and conferences) aimed at using mathematics to contributing to the betterment of humanity. (I have agreed to serve on the scientific committee to evaluate these proposals.) We launched this initiative in January and initially set the deadline for April 15, but several people who had expressed interest felt that this was insufficient time to prepare a quality proposal, so we have now extended the deadline to June 1, and welcome further applications.

See also this Mathstodon post from fellow committee member John Baez last year where he solicited some preliminary suggestions for proposals, and my previous Mathstodon announcement of this programme.