Rado Fulek: Z_2-embeddings of graphs on surfaces

Abstract:
A Z_2-embedding of a graph G on a surface M is a drawing
of G on M in which every pair of non-adjacent edges of G cross
an even number of times. A classical result of Hanani and Tutte
states that only planar graphs admit Z_2-embeddings in the plane. 
This result and its variants found many applications, most notably 
in fast embeddability testing of graphs, and
extremal and coloring problems on geometrically defined 
hypergraphs.
We survey some recent developments in the study of 
Z_2-embeddings on higher genus surfaces.

Some parts of the talk are based on joint works with J. Kyncl.