Jakub and Pavlo proved a new, strong bound on the number of squares of linear forms required to represent all suitable quadratic forms of rank r over a totally real number field. See preprint for this and more at https://arxiv.org/abs/2112.15243.
Magda Tinková was awarded the prestigious Postdoc Individual Fellowship from Czech Science Foundation, which will provide her with full funding for a 2-year position at Technical University Graz (Austria).
We (Andrew Granville and Ale, Giacomo, Pavlo, Vita) proved that there exist long sequences of consecutive real quadratic fields that all have large class numbers. The preprint is at http://arxiv.org/abs/2111.11549.