spective
WORKSHOPS
of invariant solutions and bifurcation phenomena.
Since one of the objectives of the workshop (and
of the original Thematic Program) was to bridge
mathematical analysis and scientific computations,
many of the presentations involved elements
of both. One important development which has
taken place in this field since the time of the
original Thematic Program is the emergence of
sum-of-squares polynomial optimization as a
computationally tractable approach to precisely
bounding various quantities in dynamical systems;
a day of activity in the workshop was devoted
to surveying the state of the art in this field.
In addition to the keynote lectures by Sergei
Chernyshenko, Carlo Cossu, Colm-cille Caulfield, and
Vera Mikyoung Hur, a highlight of the workshop was
the public lecture delivered to an audience of over
50 attendees by Javier Jiménez from the Polytechnic
University of Madrid. Titled Should we trust robot
scientists?, the lecture challenged the audience
to reflect on how the role that computers and
computation play in scientific discovery has changed
over the last few decades. The workshop was well
attended and the presentations were given by
researchers at various career stages. Generous time
was reserved for informal conversations, which were
very lively. There was consensus that yet another
follow-up event should be planned in the future.
The following week, key topics in cold-matter physics
and quantum chemistry were represented during
a five-day workshop focused on the two areas of
study. Several talks explored connecting application
domains, with similar mathematical and numerical
tools. The talks emphasized that the improvement
of the accuracy of mathematical models and
the efficiency of numerical schemes can
have a tremendous impact on advancing
the knowledge of quantum systems.
There was a consensus among workshop participants
that efficient high-performance computing (HPC)
techniques are needed if simulations of systems
with a very large number of degrees of freedom are
performed. This trend was illustrated by a number of
talks presenting a large variety of numerical methods
(spectral methods, finite elements, lattice Boltzmann,
and so forth). The HPC implementation of numerical
methods proved mandatory in various applications,
such as the computation of quantum vortices and
turbulence in superfluids, determination of electronic
structure in materials and molecular-dynamics
simulations in chemistry. The promising new trend
towards incorporating big data and deep-learning
techniques into simulation techniques was shown to be
a prevailing theme, introduced in several presentations.
The exchange of approaches between a variety
of fields was enabled by lively debate. Feedback
about the conference was overwhelmingly positive;
all the participants, regardless of their experience
and seniority, expressed their satisfaction with the
workshop and the ideal framework for scientific
exchange provided by the Fields Institute.
The initiative to gather specialists from quantum
physics and quantum chemistry in a workshop
fully dedicated to exchanges between these two
mathematics communities was unique to the 2016
Thematic Program, and the 2019
retrospective workshops
confirmed the value of this
method. Such encounters
can catalyze the dynamics
of these two research
fields, which have a
strategic importance due
to their applications aimed to
trigger a technological revolution
based on quantum systems.
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