Mathematical Sciences

News and events

The Department of Mathematical Sciences invites you to participate in Dynamics Day Europe conference at Loughborough University 3-7 September 2018.

Scientific Committee

David Elworthy (Warwick), Roger Grimshaw (Loughborough/UCL), Konstantin Khanin (Toronto), Carlangelo Liverani (Rome Tor Vergata) and Beatrice Pelloni (Heriot Watt).

Organising Committee

Andrew Archer, Wael Bahsoun, Gennady El, Anatoly Neishtadt, Alexander Veselov, Huaizhong Zhao

Plenary Speakers

  • Mark Ablowitz (Colorado, Boulder)
  • Viviane Baladi (IMJ-Paris)
  • Sylvie Benzoni -Gavage (Lyon)
  • Martin Hairer (Warwick)
  • Oliver Junge (Munich)
  • Edgar Knobloch (Berkeley)
  • Arkady Pikovsky (Potsdam)
  • Mary Silber (Chicago)
  • Dmitry Turaev (Imperial College)
  Monday Tuesday Wednesday Thursday Friday

7.30-8.45

9.45-9.00

Registration

Conference opening

       

9.00-10.00

Plenary talk:
Knobloch
Plenary talk:
Benzoni-Gavage
Plenary talk:
Baladi
Plenary talk:
Pikovsky

Plenary talk:
Turaev

10.00-10.30 Tea Break Tea Break Tea Break Tea Break Tea Break
10.30-12.30 Parallel sessions Parallel sessions Parallel sessions Parallel sessions Parallel sessions
12.30-14.00 Lunch
Lunch
Lunch Lunch Lunch

14.00-15.00

Plenary talk:
Silber
Plenary talk:
Ablowitz
Plenary talk:
Hairer
Plenary talk:
Junge
 
15.00-15.30 Tea Break Tea Break Tea Break Tea Break  
15.30-18.30 Parallel sessions Parallel sessions Parallel sessions Parallel sessions  
19.00     Gala Dinner    

Parallel Sessions: Venues and times

Room Mon (am) Mon (pm) Tues (am) Tues (pm) Wed (am) Wed (pm) Thu (am) Thu (pm) Fri (am)
CC011  MS13  MS13  MS13  MS7  MS7  MS7  MS15  MS15  MS15
CC012  MS11  MS11  MS1  MS1  MS1  MS17  MS1  MS1  MS1
CC013  MS3  MS3  MS3  MS3  MS3  MS12  MS3  MS3  MS3
CC021  MS10  MS10  MS10  MS10  MS5  MS5  MS18  MS18  MS18
CC029a  Cont  Cont  Cont  Cont   Cont  Cont  Cont  Cont  Cont
J001  MS8  MS8  MS8  MS22  MS6  MS6  MS6  MS6  MS6
J002  MS4  MS4  MS4  MS4  MS4  MS20  MS9  MS9  MS9
J104  MS21  MS21  MS2 MS2   MS2  MS2  MS2  MS2  MS2
SCH013  MS16  MS14  MS14  MS19  MS19        

 

 

 

 

 

 

 

 

 

 

 

MS1 Billiards. Room CC012 James France Building, no. 67 on the campus map.
MS2 Pattern formation. Room J1.04 Edward Herbert Building, no. 62 on the campus map.
MS3 Ergodic theory and dynamical systems. Room CC013 James France Building, no. 67 on
the campus map
MS4 Networks. Room J002 Edward Herbert Building, no. 62 on the campus map.
MS5 Dynamical systems methods in fluid mechanics. Room CC021 James France Building,
no. 67 on the campus map
MS6 Random dynamical systems. Room J001 Edward Herbert Building, no. 62 on the campus
map.
MS7 Interfacial waves. Room CC011 James France Building, no. 67 on the campus map.
MS8 Dispersive hydrodynamics. Room J001 Edward Herbert Building, no. 62 on the campus
map.
MS9 Nonlinear Schrodinger models and rogue waves. Room J002 Edward Herbert Building,
no. 62 on the campus map.
MS10 Quantum chaos and semi-classical dynamics. Room CC021 James France Building, no.
67 on the campus map
MS11 Transition state theory. Room CC012 James France Building, no. 67 on the campus map.
MS12 Super fluids and turbulence. Room CC013 James France Building, no. 67 on the campus
map.
MS13 Integrable dynamics. Room CC011 James France Building, no. 67 on the campus map.
MS14 Complex dynamics of quantum systems. Room SCH013 Scho eld Building, no. 74 on
the campus map
MS15 Dynamics of localized structures of nonlinear wave equations. Room CC011 James
France Building, no. 67 on the campus map.
MS16 Microlocal analysis and applications. Room SCH013 Scho eld Building, no. 74 on the
campus map
MS17 Stochastic dynamics of cancer evolution: models and data. Room CC012 James
France Building, no. 67 on the campus map.
MS18 Structure and dynamics of future energy systems: power grids as complex dynamical
systems. Room CC021 James France Building, no. 67 on the campus map
MS19 Invariant sets in dynamical systems. Room SCH013 Scho eld Building, no. 74 on the
campus map
MS20 Linking the dynamics of oscillator models to real-world networks. Room J002 Ed-
ward Herbert Building, no. 62 on the campus map.
MS21 Dynamics of active matter. Room J1.04 Edward Herbert Building, no. 62 on the campus
map.
MS22 Self-organization and self-assembly in uid-structure interactions. Room J001 Ed-
ward Herbert Building, no. 62 on the campus map.
Contributed Talks. Room CC029a James France Building, no. 67 on the campus map.

Titles and Abstracts of Plenary Talks



Speaker: Edgar Knobloch
Title: Spatially Localized Structures in Driven Dissipative Systems: Theory and Applications
Abstract: Spatially localized structures arise frequently in driven dissipative systems. In this lecture
I will describe a number of examples from different physical systems, followed by a discussion of the
basic ideas behind the phenomenon of nonlinear self-localization that is responsible for their existence.
I will illustrate these ideas using a simple phenomenological model and explain why the qualitative
predictions of this model help us understand the properties of much more complicated systems ex-
hibiting spatial localization, including those arising in uid mechanics.
Session chair: Christopher Linton

Speaker: Mary Silber
Title: Pattern formation in the drylands: vegetation patterns captured by satellite images
and by mathematical models
Abstract: A beautiful example of spontaneous pattern formation appears in the distribution of vege-
tation in some dry-land environments. Examples from Africa, Australia and the Americas reveal that
vegetation, at a community scale, may spontaneously form into stripe-like bands, alternating with
striking regularity with bands of bare soil, in response to aridity stress. A typical length scale for such
patterns is 100 m; they are readily surveyed by modern satellites (and explored from your armchair
in Google maps). These ecosystems represent some of Earth's most vulnerable under threats to de-
serti cation, and some ecologists have suggested that the patterns, so easily monitored by satellites,
may have potential as early warning signs of ecosystem collapse. I will describe efforts based in simple
mathematical models, inspired by decades of physics research on pattern formation, to understand
the morphology of the patterns, focusing particularly on topographic in uences. I will also describe
e orts at analyzing the patterns via the satellite images, which, in some cases, we can accurately align
with the aerial survey photographs from the 1950s to investigate details of the pattern evolution.
Session chair: Peter Ashwin


Speaker: Sylvie Benzoni-Gavage
Title: Whither dispersive hydrodynamics?
Abstract: Dispersive hydrodynamics refers to models of mathematical physics in which dissipative
phenomena are negligible, while wave propagation is subject to dispersion. Applications range from
water waves to super uids and nonlinear optics. Even though this has been a very active eld in the
last decades, the corresponding mathematical theory still conceals tough open questions. The lack
of damping in those models is one of the main difficulties, somehow compensated by the fact that
they are usually endowed with a Hamiltonian structure. Besides open questions, the talk will review
a series of recent results regarding stability and modulation of travelling wave solutions to a rather
general class of such models.
Session chair: Karima Khusnutdinova


Speaker: Mark Ablowitz
Title: New classes of integrable nonlocal nonlinear equations and solitons
Abstract: Solitons and the Inverse Scattering Transform (IST) are well known in the Math/Physics
community. A surprisingly large number of`simple integrable nonlocal equations have been identi ed;
their solutions, including solitons and properties will be discussed.
Session chair: Sara Lombardo


Speaker: Viviane Baladi
Title: On the measure of maximal entropy of Sinai billiards
Abstract: Sinai billiards maps and ows are uniformly hyperbolic - however grazing orbits give rise
to singularities. Most existing works on the ergodic properties of billiards are about the SRB measure
(i.e. the Liouville measure in the case of ows), for which exponential mixing is known (both in
discrete and continuous time). Another natural equilibrium state is the measure of maximal entropy.
Since the discrete-time billiard is discontinuous, the mere existence of this measure is not granted a
priori. With Mark Demers, we have recently constructed a measure of maximal entropy and shown
that it is Bernoulli and has full support. I will also discuss conditions ensuring that the measure of
maximal entropy differs from the SRB measure.
Session chair: Matt Nicol

Speaker: Martin Hairer
Title: The natural evolution loop space
Abstract: TBA
Session chair: Domokos Szasz

Speaker: Arkady Pikovsky
Title: Global modes in oscillator populations
Abstract: Systems of many interacting oscillators can demonstrate nontrivial collective dynamics:
different types of synchrony, collective chaos, chimera states. We discuss different ways to reduce the
original complex system to a low-dimensional description in terms of a few global variables (order pa-
rameters). We show how the famous Watanabe-Strogatz and Ott-Antonsen methods can be extended
by virtue of perturbative approaches.
Session chair: Christian Beck


Speaker: Oliver Junge
Title: Computational methods for global dynamics
Abstract: We survey computational methods for approximating the global long term behavior of
dynamical systems. At the core, these methods are based on an operator, the transfer operator,
which describes how probability densities on state space evolve under the dynamics. Starting with
a set-oriented approach for computing arbitrary invariant sets, we describe how to use the resulting
covering in order to obtain a nite matrix description of the transfer operator. From its spectrum,
cyclic and almost invariant (metastable) macroscopic dynamics can be detected. In the case of a
differential equation, there is an entire semigroup of these operators and it suffices to approximate
its generator in order to obtain a macroscopic description of the long term dynamics - without any
trajectory integration. For time-varying systems, these concepts can be generalized and lead to a
method for the computation of advective coherent sets, e.g. in unsteady uid ows. These coherent
sets can also be computed by a seemingly different approach based on geometric ideas, leading to
a nite-element based computational method which also works for sparse and incomplete trajectory
data. Throughout the talk, the mathematical concepts will be illustrated by computational examples.
Session chair: Gary Froyland


Speaker: Dmitry Turaev
Title: Energy transfer in slow-fast Hamiltonian systems
Abstract: We demonstrate that if a Hamiltonian systemis not ergodic for some range of parameter
values,then a slow and time-periodic change of parameters may lead to a sustained energy growth.
This principle extends to a general setting of slow-fast Hamiltonian systems: violation of ergodicity
in the fast subsystem leads to a rapid equilibration in the slow-fast system as a whole. We have a
similar phenomenon in the quantum-mechanical setting where we show that a periodic destruction
and restoration of a quantum integral leads to an exponential energy growth.
Session chair: Anatoly Nieshtadt