Algorithms in Combinatorial Topology

Series: 
Research Horizons Seminar
Wednesday, October 5, 2016 - 12:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Department of Mathematics, Georgia Institute of Technology
,  

Food and Drinks will be provided before the seminar.

For every surface (sphere, torus, etc.) there is an associated graph called the curve graph.  The vertices are curves in the surface and two vertices are connected by an edge if the curves are disjoint.  The curve graph turns out to be very important in the study of surfaces.  Even though it is well-studied, it is quite mysterious.  Here are two sample problems: If you draw two curves on a surface, how far apart are they as edges of the curve graph? If I hand you a surface, can you draw two curves that have distance bigger than three?  We'll start from the beginning and discuss these problems and some related computational problems on surfaces.