Best Lipschitz constants for mapping n points onto a grid
Michael Dymond (Birmingham)
In the 90's Feige posed the question of whether the best Lipschitz constant for mapping a square number n of points in the planar integer lattice onto the regular n times n grid is bounded independent of n. We will discuss the negative answer to Feige's question and its relation to the continuous question of solvability of the pushforward equation, a generalised form of the prescribed Jacobian equation. We further discuss a recent probabilistic upper bound on the size of these best Lipschitz constants. This is joint work with Eva Kopecká (Innsbruck) and Vojt臎ch Kalu啪a (IST Austria).
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