Submitted by jlongwor on Thu, 11/15/2012 - 11:18am.
Nov 16 2012 - 1:00pm
Nov 16 2012 - 1:50pm
In 1997 Elekes showed that if you have "many" lines in the plane containing "many" points of a cartesian product then a positive fraction of the lines should be parallel or have the same intersection point. We show that this result can be extended by considering fewer lines still containing "many" points of a cartesian product. We used this to extend a theorem of Elekes and Ronyai regarding the structure of a surface containing many points of a cartesian product. These results give a proof of a conjecture of Purdy saying that if two collinear sets in the plane give too few distinct distances then the lines are parallel or orthogonal.
Submitted by jlongwor on Thu, 11/08/2012 - 10:40am.
Nov 9 2012 - 10:00am
Nov 9 2012 - 10:50am
Pseudo Differential Operators Seminar: I will briefly review the results from previous lectures (definitions, L^2 boundedness and composition formulas) and prove the asymptotic expansion for the symbol of the Adjoint operator