Author

Florian Frick

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Preprint Sep 2026

Counterexamples to the Ramos conjecture for two hyperplanes

For every $n\ge2$, we construct $4n-2$ nondegenerate Gaussian measures on $\mathbb{R}^{6n-3}$ that cannot be simultaneously equipartitioned by two affine hyperplanes. This disproves the Ramos conjecture for two hyperplanes. Combined with known upper bounds, the construction shows that $3\cdot2^{s-1}-2$ is the least dim...

Florian Frick · 0 citations

Preprint Sep 2026

Superpolynomial lower bounds for vertex numbers of real projective space triangulations via a topological Figiel-Lindenstrauss-Milman theorem

We prove that every simplicial triangulation of real projective $d$-space has $\exp(\Omega(\sqrt d))$ vertices. Together with known constructions, this determines the minimum vertex number as $\mu_d=\exp(d^{1/2+o(1)})$. The result follows from a topological generalization of the Figiel--Lindenstrauss--Milman inequality...

Florian Frick, Kaave Hosseini, Eric Myzelev et al. · 1 citation