CECM/Math Colloquium: Wednesday October 15th at 3.30 in K9509

Speaker: Nassif Ghoussoub, PIms and UBC

Title: Morse theory up to $\epsilon$

Abstract: How to recover Morse theory (or a part of it) without the usual
compactness assumptions \`a la Palais-Smale  or the non-degeneracy conditions 
\`a la Fredholm? This important (and recurrent) problem has been successfully
addressed in various settings by Conley, Floer, Bahri and many others.In this
talk, we shall give a more primitive approach that originates in the
variational methods for solving partial differential equations. We show
that a change in the topology of the level sets of a function will always
produce an {\it almost critical point} with the right {\it approximate
Morse index}. On the other hand, this type of information can sometimes
lead to compactness and therefore to the solution of the corresponding
variational problem. This is the case for the Hartree-Fock equations and
some non-linear elliptic equations involving the critical Sobolev exponent.