Rational polygons: Odd compression ratio and odd plane coverings

Seminar

Speaker

Yuri Rabinovich (University of Haifa)

Date

15/05/2016 - 15:30 - 14:00Add to Calendar 2016-05-15 14:00:00 2016-05-15 15:30:00 Rational polygons: Odd compression ratio and odd plane coverings We show that for any rational polygon P in the plane, and any odd-sized collection of translates of P, the area of the set of points covered by an odd number of these translates is bounded away from 0 by a universal constant depending on P alone. The key ingredient of the proof is a construction of an odd cover of the plane by translates of P. That is, we establish a family of translates of P covering (almost) every point in the plane a uniformly bounded odd number of times. Joint work with Rom Pinchasi. Math building, 3rd floor seminar room (216/201) אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public

Place

Math building, 3rd floor seminar room (216/201)

Abstract

We show that for any rational polygon P in the plane, and any odd-sized collection of translates of P, the area of the set of points covered by an odd number of these translates is bounded away from 0 by a universal constant depending on P alone.

The key ingredient of the proof is a construction of an odd cover of the plane by translates of P. That is, we establish a family of translates of P covering (almost) every point in the plane a uniformly bounded odd number of times.

Joint work with Rom Pinchasi.