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  Up to dimension seven, compact (simply connected) homogeneous Einstein manifolds had been almost completely classified. The only remaining case was the six-dimensional Lie group S³×S³ ≅ SU(2)×SU(2). The Einstein equations for left-invariant metrics on S³×S³ are extremely messy algebraic equations. (See https://doi.org/10.1016/j.geomphys.2018.02.015) But now this seems to have been resolved! In https://arxiv.org/abs/2609.06425, Gu and Qi use a novel approach that I still have to understand. And...

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  Even with the current situation where editors are struggling to find reviewers for their math journals, I still think that it's a good thing referees aren't remunerated or otherwise rewarded. Otherwise by now 99% of referee reports would be written by LLMs.

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  The second exterior power of a half-spin representation of Spin(2n+4) is isomorphic to a direct sum of a bunch of exterior powers of the vector representation. Thus: \[\sum_{k=0}^{\lfloor n/4\rfloor}{2n+4 \choose n-4k} = {2^{n+1} \choose 2}.\] Might be a special case of the series multisection identities for binomial coefficients: https://en.wikipedia.org/wiki/Binomial_coefficient#Multisections_of_sums For n=3 we obtain the celebrated identity (16 choose 2) = (10 choose 3).

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  A Leibniz algebra is a nonassociative algebra that satisfies the (right) Leibniz identity: (ab)c = (ac)b + a(bc). In other words, right-multiplication by any element acts as a derivation of the algebra. This is more general than a Lie algebra, since the product need not be skew-symmetric. (The product is often written as a bracket [a,b], but I will stick with ab for now.) Since we don't require our algebra to be associative or commutative, there are many ways to arrange n given elemen...

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  They made the isospectral drums https://prismika.github.io/2026/03/01/we-made-the-isospectral-drums.html