change of schedule: prof. Tintarev's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

This seminar has been shifted from Thursday 18 to Friday 19 April


SPEAKER:
Cyril Tintarev, Uppsala

TITLE:
Cocompact imbeddings and profile decompositions: functional-analytic
theory of concentration compactness.

Abstract:
Many imbeddings of functional spaces lack compactness because of the
presence of a non-compact invariance, such as translation or scale
invariance. Loss of compactness for bounded sequences can be effectively
described with the help of this group: any bounded sequence has a
subsequence consisting of a sum of decoupled "bubbles" (by group action)
and a convergent remainder. This representation, called profile
decomposition, exists on the functional-analytic level, and the hard
analysis is involved only in the question what is the best norm for which
an absence of bubbles guarantees convergence. Successor of the classical
concentration compactness, theory of profile decompositions in its present
state has been applied to concentration analysis in dispersive equations
(Terence Tao), yields a necessary and sufficient condition for a symmetry
on a manifold to define a compact Sobolev imbedding, and shows that
Moser-Trudinger functional is weakly continuous on a unit ball $B$ in the
Sobolev norm with an exception only for some  sequences on a single
three-dimensional surface contained in the boundary of the unit ball.


Venue: Friday 19 April at 11 am in lecture room 133