Combinatorics Seminar

When: Sunday, Jan. 2, 10am Where: Schreiber 309 Speaker: Rom Pinchasi, Technion Title: Isoperimetric Inequality in the Punctured Plane

Abstract:

We consider the two dimensional plane and show that for every simple closed curve which bounds an area empty from integer lattice points, the length of the curve is greater than or equal to the area bounded by that curve times a constant $\epsilon = 1.715...$. We also show that this $\epsilon$ is best possible. The proof is generalized to the universal cover of $R^2 \setminus Z^2$ equipped with the natural lifted metric, thus providing a strengthening of the theorem in the plane.

This is a joint work with my brother, Adi Pinchasi (Tel-Aviv University).