Discrete Geometry: Noncrossing Partitions Seminar - Michael Dougherty

Event Date: 

Wednesday, April 29, 2015 -
2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Price: 

Free

Event Contact: 

Michael Dougherty

Email: dougherty@math.ucsb.edu

  • Discrete Geometry Seminar

In the 1960s, Milnor proved that certain intersections of balls with complex hypersurfaces can be expressed as fiber bundles. In particular, the complement of a central (non-affine) arrangement of complex hyperplanes is a fiber bundle over the circle. However, in even the "nicest" such setting, the braid arrangement, the homology of the fiber is unknown in general. In this talk we will discuss a way of leveraging the combinatorial structure of noncrossing partitions to create a geometrically appealing simplicial complex for the Milnor fiber. Knowledge of fundamental groups and covering spaces will be useful, although the content is otherwise introductory.