The logarithmic Brunn–Minkowski conjecture
We prove the logarithmic Brunn–Minkowski conjecture for arbitrary origin-symmetric convex bodies in every dimension. The theorem also gives the symmetric L p Brunn–Minkowski inequality for every $0\lt p\lt 1$. Combined with Saroglou's transfer theorem and a support-subspace reduction, it yields the logarithmic inequality for every even log-concave Radon measure and the scalar-dilation $(B)$-conjecture.
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Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
a proof of the logarithmic Brunn–Minkowski conjecture for origin-symmetric convex bodies in every dimension. The two-point Chowla conjecture. In EDP Reflections and Celebrations (2015), I discussed Tao’s logarithmically averaged Chowla and Elliott results and their role in solving the Erdős…