Mathematics Program Presents
Tuesday, September 12, 2017
An Introduction to Line Arrangements and the Search for Zariski Pairs
Moshe Cohen, Vassar CollegeA line arrangement is a finite collection of lines in the plane. We can study this combinatorially by looking at intersections of lines. We can study this topologically by looking at the complement (in complex projective space). We can ask if the combinatorial information forecasts the topological information. When this does not occur, we obtain two different geometric arrangements; we call this a Zariski pair. There is no such pair of up to nine lines. Examples have been found with thirteen lines by Rybnikov in 1998 and with twelve lines by Guerville-Balle in 2014. Together with Amram, Sun, Teicher, Ye, and Zarkh, we investigate arrangements of ten lines. Together with an undergraduate student Liu last year, we investigate arrangements of eleven lines.
For more information, call 845-758-7362, or e-mail email@example.com.
Time: 12:00 pm
Location: Hegeman 204