A mathematician, Paola Goatin specialises in partial derivative equations, and more particularly conservation law systems. These equations are often used to describe physical phenomena such as gas dynamics or compressible fluid flows. Hence the possibility of also being able to use them to describe changes in traffic density over time and space, as Paola successfully proposed in her ERC application.
A university career in France and Italy
Born in north-east Italy, Paola has always loved maths. After a Masters in 1995 at Padua University in partial derivative equations analysis, she decided to continue her career in research. "I decided to do something I enjoyed, although I asked myself many questions about the career prospects open to me in Italy at the time." Paola joined Prof. Alberto Bressan's team at the Trieste International School for Advanced Studies, highly renowned in the field of functional analysis, where she completed her PhD in conservation law systems. In 2000, she went to France and the École Polytechnique, where she undertook her post-doctoral studies supervised by Philippe le Floch (University Paris VI, French National Centre for Scientific Research). Three years later, she secured a position as a senior lecturer at Sud Toulon-Var University and is attached to the Toulon Institute of Engineering Sciences.
From equations to applications
Despite the substantial proportion of her time spent teaching, Paola also actively conducts research work. "With former colleagues from Paris and Italy, I started to study road traffic models, and then turned towards applications," Paola recalls. In 2008, she requested a part-time placement at Inria within the OPALE project team, where she worked towards obtaining her habilitation to advise doctoral theses, with specialists in hyperbolic approximation techniques. "I consequently submitted my European project, focusing on road and pedestrian traffic." At the time she was presenting her application to the European Research Council, she was also applying to join Inria, which she has now done. "I appreciate the organisation of the research work and I feel supported in my non-scientific tasks. That's important."
Optimising road and pedestrian traffic
How can public spaces be designed to minimise accidents when crowds are on the move, or traffic lights be positioned to ensure the smoothest possible flow of urban road traffic? These are the kind of questions, with a strong socio-economic component, that the project presented by Paola Goatin to the ERC aims to answer.
It's an interesting subject owing to its very practical applications in traffic management, and more broadly in town planning and architecture, but it also raises some exciting theoretical mathematical problems.
Paola Goatin explains. This mathematician however stands apart from the usual approaches based on modelling the movements of each car or pedestrian. "That approach can be used to study traffic at a junction or to handle the evacuation of aircraft or trains. But it is not appropriate for describing traffic across the road network for a whole town, or the movement of huge crowds." Which explains why she has adopted a macroscopic approach, taking inspiration from fluid dynamics and adapted to take account of the specific constraints of these problems. In the case of road traffic, this means modelling the changes in vehicle density in a network, an approach which benefits from a mathematical theory that has been well-developed since the 1950s.
For pedestrians, conversely, who represent a more recent field, we are confronted with a further difficulty, which is that pedestrian travel is not one dimensional (following the road) but two dimensional because the urban space is not a corridor. The corresponding mathematical theory is not sufficiently developed.
Another advantage, another scientific challenge – the macroscopic approach makes it possible to study control and optimisation problems with the aim of improving traffic fluidity (for example by modulating traffic flow with traffic lights) or to prevent or minimise accident risk (for example by judicious placing of potential obstacles to facilitate building evacuation). Here too, the researcher and her team will need to design new optimum control techniques because conventional theories are not suited to the discontinuous solutions describing such movement.