My supervisor Hamed Hatami and I have just uploaded to the arXiv two new preprints: “Block complexity and idempotent Schur multipliers” and “Block structure in boolean matrices with bounded factorization norm”. These papers are strongly related, and this blog post I’ll introduce their common background before discussing what have recently managed to prove.
Update. I was interviewed by Joyce Chung about this piece. Read the interview here.
I wrote a story back in July that I realised, upon reading it back, was entirely non-fictional (modulo the exact words used in dialogue). A lot of the things I write are semi-autobiographical anyway, so I was intending to pass it off as just another (fictional) short story. Then a couple of weeks later I saw The Malahat Review’s submission call for the Constance Rooke Creative Nonfiction Prize, and I thought I might as well enter, as it isn’t every day that I write a piece of CNF.
I’m excited to announce that my short story “The Vigil,” which appeared in Ricepaper Magazine last year, has been selected for inclusion in the anthology Best Canadian Stories 2025, which showcases the best Canadian short fiction published in 2023. If you’re interested, the book should be out in stores in a few weeks, but in the meantime you can preorder it from the publisher’s website. (But you should also consider buying it from your local independent bookshop!)
In early July of 2021, I was on a holiday with my parents in Canmore. This was the first stop in a long journey during which I planned to split off from my parents in Revelstoke, meet my university friends in Kelowna, and then drive across Canada back to Montréal, so I had brought a decent stack of books with me. In that stack was a short story collection by Margaret Atwood called Dancing Girls. The stories themselves were pretty good (honestly I don’t remember the details of most of them), but it was the first page that intrigued me. It looks like this (TeX reproduction because I don’t have access to a good digital camera right now):
Jonah Saks and I have uploaded our paper “Alternating-sum statistics for certain sets of integers” to the arXiv. We show that if ${\cal F}$ is a set family in our class, then a certain alternating-sum statistic is constant. This constant equals $-1$ in the case where ${\cal F}$ is the set of all finite primitive sets. Towards the end of the paper, we generalise the notion of primitive sets to $s$-multiple sets and show that if $s\ge 2$, then the alternating-sum statistic we study is not constant, but as $n$ increases it equals $(-1)^s {n-2\choose s-1}$.
