Lorena Aguirre Salazar discussed
patterns in a Thomas-Fermi
theory for molecular ionization.
Liquid crystal models constituted
an important theme of the
workshop, and many talks
involved the development
of geometrical singularities
in nematic liquid crystals.
This is a very active subfield
to which Sternberg has
extensively contributed.
Dmitry Golovaty and Michael
Novack presented work with
Sternberg on the isotropic-
nematic transition for Landau-de
Gennes models. Tiziana Giorgi
spoke about transitions in bent-
core smectics, and Dan Phillips
discussed surface defects for
nematics with slab geometry.
Patricia Bauman presented
regularity results for a more
physically justified functional with
a singular Maier-Saupe potential.
Xie Xiao spoke on dynamics of
flows in Campanato-Sobolev
space, including nematics.
Ginzburg-Landau functionals
presented another common
theme throughout the meeting.
Dan Spirn gave a thoughtful talk
on nucleation of vortices in a
superconductor, an open problem
of long standing. Étienne Sandier
and Tien-Tsan Shieh both spoke
of phase separation in a Bose-
Einstein condensates, and Andrés
Contreras discussed stability of
domain walls. As Bose-Einstein
condensates involve both vortices
and domain walls, these talks
blended nicely with those on the
Cahn-Hilliard models for phase
transitions (which were the
subject of Sternberg's thesis).
In the Cahn-Hilliard context,
Yoshi Tonegawa presented sharp
estimates on convergence of the
singular limits to constant mean
curvature surfaces, and
Nick Alikakos showed new results
on the fine structure of solutions
near junction points. Several
speakers also presented results on
the dynamics of interfaces.
Max Morini gave new results
on the limiting dynamical
problem, flow by mean
curvature, for anisotropic and
crystalline interfaces. Maria
Westdickenberg discussed a
different dynamical issue for
Cahn-Hilliard: rates of relaxation
of the energy to a minimizer.
Finally, Shuichi Jimbo introduced
the interesting concept of
traveling fronts for Allen-
Cahn along Y-shaped graphs.
Participants also learned about
other fascinating directions in the
calculus of variations, including
Gershon Wolansky's new analysis
of the Gilberg-Steiner problem for
optimal networks, and progress
in 3D Voronoi tesselations by Xin
Yang Lu. Xavier Lamy presented
results on entropy production
for the Eikonal equation, with
connections to the Aviles-Giga
functional, a common thread
in many talks across the
various subfields. David
Padilla-Garza expanded
on Bob Kohn's talk on
wrinkling of sheets, and
in a similar vein, Cy Maor
discussed non-Euclidean
thin bodies (including
leaves and vegetables).
Nonlocal elastic energies
and peridynamics were
introduced
by PhD student James
Scott, and Salvatore
Stuvard showed how
Plateau's problem
arises in a singular limit
from capillarity. The
workshop reflected
Sternberg's joyous and
relaxed approach to mathematics,
and was exceptional for the
congenial atmosphere and high
level of communication and
discussion during breaks. Many
of the participants had significant
interaction with Sternberg,
either as coauthors, students,
or colleagues, and nearly all of
the audience was familiar with
recent developments in the
diverse topics even if they hadn't
published in a specific area, so the
question periods were quite lively.
The meeting was enhanced
by the large number of junior
researchers who presented results
on a diverse range of variational
problems, from Voronoi cells
to Thomas-Fermi functionals to
capillarity. Among the speakers
were four PhD students, five
postdoctoral fellows, and
five pre-tenured faculty;
the younger generation
was well represented,
and the future of
the calculus of
variations is
in good
hands.
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