iiinova — where your digital self keeps evolving

Sam Power @spmontecarlo.bsky.social · 30/09/2026

nice to see it framed so clearly

Sam Power @spmontecarlo.bsky.social · 27/09/2026

One of my favourite tweets of yesteryear is the attached. I think that in (maths) research we don't talk so often about the (pretty ubiquitous) experience of discovering something in one's one time, and then coming to the realisation that it's not as new as one might have hoped.

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Sam Power @spmontecarlo.bsky.social · 26/09/2026

Saturday Morning Breakfast Simons

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Sam Power @spmontecarlo.bsky.social · 23/09/2026

Pilea-repotting day is always a joy. From 2 pots at the start of the day, to 7 at the end!

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Sam Power @spmontecarlo.bsky.social · 23/09/2026

A point which I continue revisiting in recent conversations about "what is to become of (mathematics) research?" is that there remains no scarcity of interesting things to wonder about, that many things should certainly still be written down, disseminated, and that this is "what it's all about".

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Sam Power @spmontecarlo.bsky.social · 22/09/2026

lots of discrepancy theory on arXiv these days

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Moritz Schauer @mschauer.bsky.social · 21/09/2026

The σ-algebra viewpoint also gives a nice form of the Chinese remainder theorem: for pairwise coprime n₁, …, nₖ it holds σ(x mod n₁, …, x mod nₖ) = σ(x mod n₁⋯nₖ). Knowing the residues separately is exactly the same information as knowing the residue modulo the product.

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Sam Power @spmontecarlo.bsky.social · 21/09/2026

a few papers from the last months which I enjoyed (~chronologically):

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Sam Power @spmontecarlo.bsky.social · 19/09/2026

Metropolis-Ådjusted for your comfort

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Sam Power @spmontecarlo.bsky.social · 16/09/2026

(from www.its.caltech.edu/~matilde/AIm..., links to .pdf)

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Sam Power @spmontecarlo.bsky.social · 12/09/2026

Conceding a priori that I'm relatively thin-skinned, I'm finding it fairly unbearable to read most social media takes about the "Severe Misalignment of AI in Mathematics". I guess that this could be anticipated (most people are not embedded in the world of mathematics), but it's all felt very grim.

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Sam Power @spmontecarlo.bsky.social · 11/09/2026

connecting disparate literatures

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Sam Power @spmontecarlo.bsky.social · 04/09/2026

Awful / True: the Wasserstein-optimal interpolation between (the uniform measures on) convex sets can induce non-convex supports in d > 1.

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Sam Power @spmontecarlo.bsky.social · 02/09/2026

Arrived at Neufchâteau-sur-Tyne for the week's workshop! Exciting times

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Sam Power @spmontecarlo.bsky.social · 31/08/2026

It's not so surprising, but it's good to know!

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Sam Power @spmontecarlo.bsky.social · 29/08/2026

Learned today: let X_a be a positive stable random variable of index a, and let Y_a = log X_a. Then Y_a has a log-concave law iff a < 1/2, per a result of Thomas Simon.

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Sam Power @spmontecarlo.bsky.social · 26/08/2026

It's really a fascinating time for research (in maths, let's say) and kind of shocking how palpably one can feel different things changing. One could quickly understand that LLM tools really shift the floor on what sorts of calculations can now be considered "routine", as a basic example.

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Sam Power @spmontecarlo.bsky.social · 25/08/2026

Suspicious minds at Bristol Museum and Gallery.

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Sam Power @spmontecarlo.bsky.social · 21/08/2026

A small note on the "Robustness of random-walk Metropolis for steep potentials", now online at arxiv.org/abs/2608.20279. The starting point is that typical analyses of MCMC methods require structural assumptions on the negative-log-density of the target which prevent it from changing too rapidly.

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Sam Power @spmontecarlo.bsky.social · 20/08/2026

Lovely paper of Azé-Penot from 1995 on "Uniformly convex and uniformly smooth convex functions", with a few great definitions and a deluge of consequences.

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Sam Power @spmontecarlo.bsky.social · 18/08/2026

A rare original contribution to our interior decor.

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Sam Power @spmontecarlo.bsky.social · 17/08/2026

registration is still open for this workshop for another week or so - hoping to see many of you there!

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Sam Power @spmontecarlo.bsky.social · 03/08/2026

Back in my "watching Simons Institute live-streams" era (www.youtube.com/@SimonsInsti...). Very influential on me as a curious PhD student, influential once more as a guy with some free time in the summer!

youtube.com

Simons Institute for the Theory of Computing

The Simons Institute for the Theory of Computing is the world's leading venue for collaborative research in theoretical computer science. Established on July 1, 2012, the Institute is housed in Calvin...

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Sam Power @spmontecarlo.bsky.social · 01/08/2026

Always interesting to see the different responses to the various items of maths news as they come out. I feel like I find it important to keep reminding myself that even for fairly proximate fields to mine within maths, there are lots of internal cultural aspects on which I'm not well-informed.

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Sam Power @spmontecarlo.bsky.social · 30/07/2026

Just to give some context: let F be a function that is reasonably continuous but not quite Lipschitz (e.g. Hölder cts). Then, define F_t (x) = sup { F(y) - t || x - y|| }. Then F_t is t-Lipschitz, and pointwise, F(x) < F_t (x) < F(x) + c_t for some constant offset c_t.

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Sam Power @spmontecarlo.bsky.social · 25/07/2026

Lots of interesting bits and pieces cropping up in (what I've encountered of) Tao's ICM talk. I do find that this aspect of 'digestion' of mathematics is generally quite exciting to me, particularly in terms of revisiting established work. (I do understand why it's less lucrative in the short term)

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Sam Power @spmontecarlo.bsky.social · 24/07/2026

A pair of notes which review and optimise a couple of fun (and by now, reasonably well-established) techniques for showing the 'contraction-on-average' property for stochastic systems, focusing on problems for which the 'obvious' metrics do not contract. (links below)

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Sam Power @spmontecarlo.bsky.social · 23/07/2026

The semi-answer one can also give here is that many of them were also interested in entropy - though often a different entropy in each case!

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Sam Power @spmontecarlo.bsky.social · 22/07/2026

The connection: despite working in dramatically different areas of mathematics, all had sufficient overlap with the work of A.N. Kolmogorov that they contributed to an obituary volume reviewing his contributions to their area.

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Sam Power @spmontecarlo.bsky.social · 22/07/2026

a fun trivia: what connects these mathematicians?

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Sam Power @spmontecarlo.bsky.social · 16/07/2026

(presumably) late to the game, but have been reading a little bit about { Proof Theory / Proof Mining / Skolemization } this afternoon, which has been sort of interesting, especially as someone with a bit of a taste for quantitative results and so on.

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Robin Ryder @robinryder.bsky.social · 08/07/2026

I have just resigned from the board of "Statistics and Computing", along with 17 other Associate Editors. This was a difficult decision: this great journal has published many tremendous articles under the leadership of EiC Ajay Jasra, and before him David Hand, Gilles Celeux, and Mark Girolami.

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Sam Power @spmontecarlo.bsky.social · 07/07/2026

interesting stuff here: x.com/mehtaab_sawh..., and a bit funny to see the Random Walk Metropolis show up in this context. some inspiration for me to try read it properly and learn something new!

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Adrien Corenflos @adriencorenflos.bsky.social · 02/07/2026

New version available at the same address! We bit the bullet and extended the work to consider arbitrary numbers of blocks, discrete spaces, parallel/systematic/random scan CAVI within a unified framework. Applications now include statistical physics models and others! arxiv.org/abs/2605.30253

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Sam Power @spmontecarlo.bsky.social · 27/06/2026

Having a nice period at the moment wherein working through the details of basic examples (or examples for basic techniques) points neatly in the direction of new results, either in the sense of suggesting proofs in the general case, or at least in the sense of "it's worth following up on this".

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Sam Power @spmontecarlo.bsky.social · 20/06/2026

Meaningless grumble: I wish that the "forward process" / "reverse process" terminology for diffusion models had instead been "noising process" and "denoising process". Feels a bit related to how I find ambiguity in the use of "top-down" and "bottom-up" w.r.t. neural networks.

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