FEATURE
Workshop on New Trends in Variational Models:
From Superconductors to Liquid Crystals
June 17-21, 2019 • Fields Institute
Organizers: Stan Alama and Lia Bronsard (McMaster University), Robert Jerrard (University of Toronto),
and Ihsan Topaloglu (Virginia Commonwealth University).
Historically, the calculus of variations is where
geometry and analysis meet physics. Geometrical
ideas provide a framework to study applied
problems, physical insights suggest solutions and
the analyses of these solutions, in the
form of nonlinear partial differential
equations and measure theory.
Several exciting avenues of
research today continue this
tradition, which extends to new
applications in materials science,
biology, and physiology. This
workshop was at once a showcase
for new methods and results in
variational problems and a celebration of an
influential and unifying mathematician,
Peter Sternberg, on the occasion of his 60th birthday.
Robert V. Kohn set the tone for the conference with
his opening talk on wrinkling of elastic sheets. A
difficult problem in elasticity, wrinkling combines
all of the elements of ground breaking variational
problems and presents daunting analytical
challenges. Kohn is one of the most versatile
researchers in the calculus of variations who has
long been a trend-setter in the field. As Sternberg's
thesis advisor, Kohn began with a timeline of
12
Sternberg's career with photos and anecdotes.
Sternberg's longtime collaborator, Koby Rubinstein,
also presented work on a new and challenging
application of classical mathematics, the role of
caustics in human vision. Geometrical
optics forms an important part of
mathematical history, and its
application to understanding
the eye and optometry
has been reinvigorated by
Rubinstein's recent work.
Several speakers addressed
the blossoming area of
patterns in nonlocal interaction
models. Ihsan Topaloglu gave an
overview of recent progress in problems
of swarming, and Rustum Choksi
described the effects of anisotropy in the short-range
interactions. Andrew Bernoff discussed dynamical
models for the fascinating group behavior of locusts.
Recent PhD, Chong Wang, presented pattern
formation in block copolymers, mathematically a
nonlocal isoperimetric problem. Alex Misiats also
spoke on pattern formation in various nonlocal
contexts, and Kevin Zumbrun gave an overview
on patterns in problems driven by convection.