Best Lipschitz constants for mapping n points onto a grid

  • 15 November 2023
  • 2pm-3pm
  • Sch 1.05
  • Michael Dymond

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 Vojtěch Kaluža (IST Austria).

 

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