**Report on the CHAMPS (Chemistry and Mathematics in Phase Space) Workshop**

**19th March 2019 – “Discovering Phase Space Structure and Reaction Mechanisms from Trajectory Data Sets” held at Engineers House, Clifton Bristol. **

This one day workshop was very much in the spirit of the CHAMPS project in that it brought together a group of chemists, mathematicians, and physicists all concerned with different aspects of the fundamental problem of revealing the phase space structures governing reaction dynamics using trajectory based diagnostics. The trajectory based diagnostic used by most of this group was the method of Lagrangian descriptors (a brief description of this approach was given in https://champsproject.com/2018/03/01/lagrangian-descriptors-from-fluid-dynamics-to-mathematics-to-chemistry/). This method has emerged as a flexible and “easy to code” method that can be used in a wide variety of settings relevant to chemical reaction dynamics.

Ana Mancho gave the first talk and discussed the basic ideas behind the method of Lagrangian descriptors and the different settings in which they can be applied. In particular, it was demonstrated how they could be applied to complex data sets in geophysical fluid dynamics settings. She was followed by Victor Garcia Garrido how the method could be applied in higher dimensional settings in order to detect periodic orbits and normally hyperbolic invariant manifolds (NHIMs) in general. Next Florentino Borondo showed how the method of Lagrangian descriptors could be applied to a study of lithium cyanide isomerization. He showed how the method revealed the stable and unstable manifolds of a hyperbolic periodic orbit that mediated the isomerization reaction. Intriguingly, he demonstrated the existence of a parabolic periodic orbit in the reaction region and argued that it played an important role in the isomerization reaction. The full implications of this observation required further study. Rigoberto Hernandez showed that the method of Lagrangian descriptors could be extended to completely new situations for reaction dynamics. In particular, he considered dissipative systems where the time dependence is stochastic and driven systems where the dividing surfaces vary in time. This theme was extended by Fabio Revuelta who considered the situation where the environment exhibits memory effects and is modelled by colored noise. Thomas Bartsch considered the reaction dynamics of a system with three reactive channels that is known to be strongly chaotic at all energies—the monkey saddle. He discussed the phase space structures controlling reaction dynamics in this situation. Joerg Main concluded the main talks by discussing how neural networks could be used to reveal the phase space structures, such as NHIMs, that govern the reaction dynamics. He showed how this approach could be used to locate time dependent NHIMs in driven systems and, from this, compute rate constants in multidimensional systems.

The day was concluded by a lively series of “lightning talks” (20 slides, 15 seconds per slide, for a total of 5 minutes) presented by the CHAMPS postdocs.

The small size of the workshop encouraged much interaction amongst the participants and encouraged further collaborations amongst the participants. We hope to hear more about the fruits of these interactions in a follow-on workshop in the near future.