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We use symplectic techniques to obtain partial results on Mahlers conjecture about the product of the volume of a convex body and the volume of its polar. We confirm the conjecture for hyperplane sections or projections of $ell_p$-balls or the Hanner polytopes.
We study some particular cases of Viterbos conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands depending o
A union of an arrangement of affine hyperplanes $H$ in $R^d$ is the real algebraic variety associated to the principal ideal generated by the polynomial $p_{H}$ given as the product of the degree one polynomials which define the hyperplanes of the ar
During the conference held in 2017 in Minneapolis for his 60th birthday, Gennady Lyubeznik proposed the following problem: Find a complete local domain and an element in it having three minimal primes such that the sum of any two of them has height 2
The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Grobner bases pass to the quotient and when they can be lifted. The main difficulty to overco
Let $X$ be the mosaic generated by a stationary Poisson hyperplane process $hat X$ in ${mathbb R}^d$. Under some mild conditions on the spherical directional distribution of $hat X$ (which are satisfied, for example, if the process is isotropic), we