Featured Speaker:
Prof. FangHua Lin, Courant Institute,
NYU.
"These two lectures will address some
analytical and topological issues concerning Sobolev mappings between
manifolds.We shall discuss local and global
topological obstructions for smooth maps to be strongly dense or to
be weakly sequentially dense in Sobolev
mapping spaces,and the topology of Sobolev mappings.We shall also
outline a generalized varifold theory for
Sobolev mappings and their applications in variational problems."
Invited Speakers:
Prof. Robert Hardt, Rice University
Size Minimization and Approximating Problems
(Thierry De Pauw (Orsay) and Robert Hardt (Rice))
"A k dimensional rectifiable current
is given by an oriented k
dimensional rectifiable set M
together with a positive integervalued density function D
. The mass of the
current is then simply the integral of
D over M (with respect to k dimensional Hausdorff
measure). In 1960
Federer and Fleming proved the existence
of a rectifiable current of least mass for a given boundary. For
q in
[0,1] , the qmass of
the current is the integral of D^q over M .
The case q = 0 corresponds
to size , introduced by Almgren as a way of using currents to model
soap films.
We will discuss the existence of a rectifiable
current of least qmass for a given boundary. For that purpose
we
make use of scans which are
certain functions arising as limits of slices of rectifiable currents."
Prof. Yisong Yang , Poltytechnic Unversity
and IAS (Princeton):
Nonlinear Problems in BornInfeld
Theory
"In 1933, M. Born and L. Infeld developed
a geometric theory of electromagnetism to accommodate a finiteenergy
point electric charge modeling the electron.
Recently, this theory has become one of the major focuses of theoretical
physicists due to its relevance in superstrings
and supermembranes. Mathematically, the BornInfeld theory presents
new challenges to analysts. In this talk,
we study the Bernstein problems for minimal surface equations, the existence
of static KleinGordon waves in arbitrary
dimensions, and the existence of cosmic strings, in the framework of the
BornInfeld theory."

