Columbia Mathematics Department Colloquium

"On fake projective planes"



(Purdue University)

A fake projective plane is a smooth complex surface which has
the same Betti numbers as the complex projective plane but not
 hiholomorphic to it.  These are surfaces with the smallest Euler-Poincare
 characteristic among smooth surfaces of general type.The first example
 was constructed by Mumford and a few more were found later.  The main
 goal of the talk is to explain the recent work of Prasad and myself
on classification and construction of fake projectiveplanes in each class. 
The final result is a consequence of techniques in geometry, number theory,
algebraic groups and computational methods.  We will also mention some
further studies and generalization of the results.

  April 16th, Wednesday, 5:00-6:00 pm
Mathematics 520
Tea will be served at 4:30pm