Date:
Mon, 25/10/202116:00-17:00
Location:
https://huji.zoom.us/j/87501314802?pwd=aERnWW5XSzRzU3hpc1VTOHorRGFMdz09
When: Monday October 25th, 2021, 4PM (Israel time)
Where: Zoom
Link to Zoom:
https://huji.zoom.us/j/87501314802?pwd=aERnWW5XSzRzU3hpc1VTOHorRGFMdz09
Speaker: Shira Zerbib (Iowa State University)
Title: Line transversals in families of connected sets in the plane.
Abstract:
We prove that if a family of compact connected sets in the plane has the property that every three members of it are intersected by a line, then there are three lines intersecting all the sets in the family. This answers a question of Eckhoff from 1993, who proved that under the same condition there are four lines intersecting all the sets. We also prove a colorful version of this result under weakened conditions on the sets, improving results of Holmsen from 2013. Our proofs use the topological KKM theorem. Joint with Daniel McGinnis.
Where: Zoom
Link to Zoom:
https://huji.zoom.us/j/87501314802?pwd=aERnWW5XSzRzU3hpc1VTOHorRGFMdz09
Speaker: Shira Zerbib (Iowa State University)
Title: Line transversals in families of connected sets in the plane.
Abstract:
We prove that if a family of compact connected sets in the plane has the property that every three members of it are intersected by a line, then there are three lines intersecting all the sets in the family. This answers a question of Eckhoff from 1993, who proved that under the same condition there are four lines intersecting all the sets. We also prove a colorful version of this result under weakened conditions on the sets, improving results of Holmsen from 2013. Our proofs use the topological KKM theorem. Joint with Daniel McGinnis.