Reconstruction Problems in Geometry

Research Horizons Seminar
Wednesday, September 3, 2014 - 12:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech Math Department
Here is a classical theorem.  Consider a bijection (just a set map!) from the Euclidean plane to itself that takes 0 to 0 and takes the points on an arbitrary line to the points on a (possibly different line).  The theorem is that such a bijection always comes from a linear map.  I'll discuss various generalizations of this theorem in geometry, topology, and algebra, ending with a discussion of some recent, related research on the topology of surfaces.