Arrangements of lines: when the combinatorics fails to understand the topology

01/26/2016 - 12:15pm
01/26/2016 - 1:10pm
Speaker: 
Moshe Cohen (Technion - Israel Institute of Technology)
Abstract: 

Zariski gave a pair of sextics with the same types of singularities, but whose complements have different fundamental groups. This motivates the search for a similar "Zariski pair" of line arrangements: two with the same combinatorial intersection data but whose (complex projective) complements have different fundamental groups. Only one minimal case has been found so far: Rybnikov produced one with thirteen lines in 1998 by gluing two smaller arrangements together. No such pair exists on nine or fewer lines. Together with Amram, Sun, Teicher, Ye, and Zarkh, we investigate arrangements of ten lines using the language of matroids. This talk is accessible to those without backgrounds in combinatorics, topology, or algebraic geometry.

Where: 
Millikan 2099, Pomona College
Misc. Information: 

There will be the seminar organizational meeting at 12:00 noon, right before the talk. Everyone is welcome!