Paul Vigneaux: The Mountain Mathematician
By: Pacific Institute For The Mathematical Sciences
Tags: Math, Physics, Science, Research, Interview

Paul Vigneaux: The Mountain Mathematician

The PIMS-CNRS International Research Lab (IRL) facilitates connections between France and Canada through transatlantic research opportunities. This is the story of one researcher who made that journey.

By Jimmy Fryers

For the last 12 months, Paul has been a welcome addition to the PIMS research community at our University of British Columbia site. As his CNRS sabbatical comes to an end and he transitions back to his home university, ENS de Lyon, Paul took some time to reflect on his experience at PIMS and the progress he made on his important research.

PIMS-CNRS UMI Labs

CNRS is one of the major government agencies dedicated to research in France. As part of its many missions, CNRS has a program to send French academics overseas to conduct collaborative projects. These global research opportunities are facilitated through a network of International Research Labs, called CNRS UMIs, and PIMS is one of these labs.

Paul enjoying the vast outdoor opportunities in and around Vancouver, BC

As Paul explained, “when someone from France wants to go on sabbatical abroad, they apply using a specific framework through the UMI of the CNRS. In mathematics, there are 10 of these International Research Labs around the world: for example, there’s one in Rio de Janeiro where Étienne Ghys is a regular visitor, there’s one in the Netherlands, and one in India.”

The Line of Best Fit

Of all the overseas lab locations available to Paul, PIMS-UBC was the best fit for his research, “It was very natural from a scientific point of view,” Paul said. “Professors Ian Frigaard, Anthony Wachs and I had common interests in the field of viscoplastic fluids. These fluids can be rigid like solids but also flow like liquids, such as toothpaste or fresh concrete.

“We originally met through scientific literature and then at conferences. At UBC there is a really dynamic group of people working on this subject in the Complex Fluid Lab, so it was natural for me to design a research project to come to PIMS and work with them directly,” Paul reflected.

By facilitating these sabbaticals, the CNRS and their partner institutes like PIMS, are not just promoting advances in research but fostering international connections of experts in particular fields, leading to long-term collaborations.

Prof Wachs highlights how this program develops international partnerships and promotes continuing relationships, “we spent most of the year with Paul exploring and identifying research questions that we could solve together and that could lead to a sustained long-term collaboration.”

For the Common Good

The positive benefits of international sabbaticals are not just felt at the personal or team level. There were institutional outcomes attributed to Paul’s presence at UBC.

Paul at work at ENS de Lyon, France

As Prof. Wachs explained, “the France-Canada partnership around mathematical science-based research through the PIMS-CNRS UMI (IRL) not only enables us to temporarily bring research skills that we might not have to UBC to advance research projects, but it also gives us opportunities to learn new skills while collaborating with our visitors.

“The diversity of approaches in mathematical science-based research, as in any other field of research, is a necessary key to success.”

The Benefit to Research

I asked Paul to explain how his time at PIMS benefitted his work, and he was quick to reply with his usual enthusiasm, “I was able to dedicate more time to research, which was possible due to the fact I had less teaching responsibilities during the sabbatical,” said Paul.

Dedicating more time to directly work on a specific research project has obvious benefits, but as Paul emphasizes, an extended sabbatical facilitates additional growth opportunities, “I had time to study different modelling and mathematical methods related to my main research area of viscoplastic fluids. I wouldn’t have had the time to be able to do that without the CNRS PIMS sabbatical. I also had the opportunity to directly discuss things with my colleagues, which was great input and couldn’t have happened if I was in France.”

Real-World Impact

Paul doesn’t fit neatly into either the theoretical, pure math domain or the area of ‘real-world,’ applied math — he keeps his feet in both camps:

“Generally speaking, while at PIMS I was working on mathematical models which describe complex fluids and two potential applications: geophysical, for example, avalanches; and another which is more theoretical, where we study variations of these equations in order to describe these fluids and what the models can teach you about their behaviour. Significant advances have been made to understand them but many things remain totally unknown, so it’s a really rich field.” Paul explained.

Paul (left) probing terrain on the slopes of Chamonix, Mont-Blanc Massif in France. His research is helping advance the models used to predict avalanche flows.

In the area of viscoplastic fluids and, specifically, avalanches, the two areas of applied and theoretical math coalesce and, through Paul’s efforts, build toward making a direct impact in reality:

“I am involved in mathematics in collaboration with physicists who want to gain insights into the phenomena of complex fluids with the help of mathematical simulations,” said Paul.

“With avalanches, we’re trying to give a model that is more and more accurate, which is very difficult; it’s extremely hard to construct an accurate equation for avalanches because snow is a really complex material and we’re really far from reality right now. However, people are already using models to make predictions on avalanches which are being used in practical applications.

“The people in the Institut national de recherche en sciences et technologies pour l’environnement et l’agriculture (IRSTEA) are concerned with environmental issues in France. The staff is made up of theoretical scientists and state engineers who are making studies on avalanche paths in French mountain cities like Chamonix and playing a major role in the design of risk prevention plans.