Lorentz Center

International center for scientific workshops

International center for scientific workshops

Current Workshop | Overview | Back | Home | Search | | ||||||||||

## Integrability and Isomonodromy in Mathematical Physics |

7-11 July 2014
The interest
in integrability started to grow in the middle of the
twentieth century. In that time Fermi,
Pasta and Ulam performed numerical experiments with
an anharmonic one- dimensional
lattice and observed to their surprise not a steady continuous flow of energy from the first
mode to the higher ones, but more an exchange of energy, essentially, among only a
certain few. Their work
inspired, on one hand, M.Toda to start the search for
nonlinear lattices that are
susceptible for further mathematical analysis. He considered systems of
one-dimensional particles
where the equations of motion of each particle are determined by a potential
de- pending only
of the distance to the particle on the left and the distance to the particle on
the right. On the
other hand, Kruskal and Zabrusky
made a continuous model to understand the
phenomenon observed by Fermi, Pasta and Ulam, where
the equations of motions in the
approximation up to the second order in the distance between the springs,
reduced to a known
nonlinear partial differential equation: the Korteweg-de
Vries equation. Starting with these
two lines of research, the impact of integrability
has been growing ever, since with a great
impact on mathematical physics. The theory of
isomonodromy deformations of rational connections
over P1(C) even has a longer
history. Pioneering work was done in the beginning of the twentieth century by
R. Fuchs and L.
Schlesinger, then it was dormant for around fifty years, till the work of the Kyoto school
of Sato made it fully alive in the late seventies, culminating in their series
of papers on
holonomic quantum fields. Both Integrability and Isomonodromy
are topics that still play an important role in various areas
of Mathematical Physics. We have chosen to focus on five topics, to which members of
the Universities of Amsterdam and Utrecht, the International Laboratory of Representation
Theory and Mathematical Physics (HSE) in Moscow and the Bogoliubov Institute in
Kiev have contributed significantly.
The various
days of the conference were each centered around a common theme. To make the workshop
also accessible for young researchers, we asked experts in each of these topics to give an
instructive presentations that prepared them for the more specialized lectures. Besides that
we also organized working sessions for young researchers to support these addresses.
All in all, the ratio between instructional and specialized lectures was one to
one. The themes
were: 1)
Associativity equations 2) Quivers,
gauge theories and integrable systems 4)
KZ-equations and their quantum version 5) Classical
and quantum spin chains
The program
was attended by 59 participants from England, France, Germany, Italy, Japan, the
Netherlands, Russia, Ukraine and the US, showing the broad international
interest in and scope of the
workshop. Among them were 25 young researchers and 10 female participants.
At the end of
the conference and afterwards at later encounters, we obtained very positive reactions on
our workshop: many participants told us that this workshop formed a source of
inspiration for them, leading to new ideas and yielding various new cooperations that will result
in joint papers and activities. More concretely, this fall it led to an
application in Brussels
for a joint program in which the theme of the conference formed a key issue. Furthermore,
we were offered the possibility to bring out a special issue of Theoretical and Mathematical
Physics on the topic of the conference.
The
conference was financially made possible by the support of the following
institutions or organizations: ·
The International Laboratory of Representation Theory
and Mathematical Physics at the National
Research University, HSE, in Moscow ·
Foundation Compositio ·
Cluster
Geometry and Quantum Theory ·
Research School Wonder Last, but not
least we like to express our gratitude to the staff of the Lorentz Center, in particular
Henriette Jensenius, Mieke Schutte and Yousra Jaddour
for their guidance, help and
support at the whole process of organizing this workshop. All participants were impressed by the pleasant ambiance at the Center and
the excellent support from its sta.
[Back] |