Rudolf Winestock @winestock@qoto.org

Tamar Ziegler and I have just uploaded a short #NumberTheory paper to the #arXiv titled "infinite partial sumsets in the primes". https://arxiv.org/abs/2301.10303 The main result is that there exist two increasing sequences \(a_1 < a_2 < \dots \) and \(b_1 < b_2 < \dots\) such that a_i+b_j is prime for all i<j. The argument uses the Maynard sieve and an intersectivity lemma of Bergelson. I discuss this result further on my blog at https://terrytao.wordpress.com/2023/01/26/infinite-partial-sumsets-in-the-primes/

I'm going to give a couple of talks about the 'tenfold way' in early February. One is in Nicohl Furey's seminar Algebra, Particles, and Quantum Theory on February 6, available online:

https://researchseminars.org/seminar/AlgebraParticlesFoundations

The tenfold way is a beautiful piece of math that originated in condensed matter physics. I want to understand it better before I give my talks!

(1/n)

@robin One more thought:

PDFs keep eating our lunch in the "web documents" space, since browsers don't have an ePub option in the "Save As" menu.

I recall there is a long and winding history underpinning all of this, but saving pages as ePubs ought to be at least an option, if not the norm.

Perhaps Mathstodon can be a place to note some folklore #MathTricks that are useful but too trifling to devote an entire paper to. Here's one (that I recalled on browsing MathOverflow https://mathoverflow.net/questions/435728): If one is trying to prove a Hilbert space identity or inequality which is invariant under a unitary group action, one can often reduce "for free" to the irreducible components of that group action. (1/2)

Memes can efficiently (and memorably) convey mathematical relationships; for instance, in https://mathstodon.xyz/@tejotaefe/109410012839349418 the "spiderman pointing" meme conveys "the following are equivalent". As another example, one could imagine the enclosed "Spongebob" meme being used to describe a toy result, a weak version of a theorem, and a strong version of a theorem respectively. Would readers like to contribute further examples? I could see myself using one in a talk one day (with attribution, ofc).

QWERTY? AZERTY?

PFUGQ !

https://youtu.be/_nMFxBRRXR0?t=144

(1925 alternative typewriter)

What are the biggest mysteries in fundamental physics, and how are we doing at solving them?

On Tuesday November 29 at 6 pm UK time I'm giving a public talk about this!

In-person seating is filled up, but you can attend free on Zoom if you register here:

https://www.icms.org.uk/events/2022/public-talk-mysteries-fundamental-physics

(1/2)