“We are building a dynamic scientific collaboration network that will strengthen ties between France and Italy”

The CNRS’s second International Research Laboratory (IRL) in Italy1 , the Ypatia Laboratory of Mathematical Sciences (LYSM), was created on December 10, 2021. What are its objectives?

Giorgio Patrizio2 : After more than twenty years of working together, the CNRS and the Istituto Nazionale di Alta Matematica (INdAM) have created the Ypatia Laboratory of Mathematical Sciences (LYSM) to build a dynamic network of scientific collaboration that will strengthen ties between our two countries in the field of mathematics. It will promote long-term stays for French and Italian mathematicians, organise scientific conferences, facilitate co-supervised doctoral theses between France and Italy, and fund assignments for doctoral fellows. LYSM first emerged in 2017 through an agreement between the CNRS and INdAM3 , the research organization that manages, promotes, and coordinates mathematical research in Italy. One of INdAM’s strategic goals is to develop and sustain contacts and collaboration between the Italian mathematical community and international partners. The creation of the Ypatia Laboratory is firmly in keeping with the framework of this activity. The new IRL will rely on a consortium that brings together laboratories established in some thirty French and Italian universities. The launch conference will bring them together in June (see boxed text).

• 1The first IRL in Italy, Fibonacci, was also in the field of mathematics, and came to a close in late 2020.
• 2Born in 1956, Giorgio Patrizio received his Ph.D. in Mathematics from the University of Notre Dame in 1983, under the supervision of Wilhelm Stoll. His research interests are in the field of several complex variables and complex differential geometry. He has served as a Full Professor of Geometry at the University of Firenze since 1995, and previously held the same position at the University of Roma Tor Vergata. He has been a visiting professor or invited research fellow at numerous universities and scientific institutions. Giorgio Patrizio has been the President of the Istituto Nazionale di Alta Matematica (INdAM) since 2015.
• 3At the time the LYSM was established as an International Associated Laboratory (LIA), a kind of structure that no longer exists today.

This IRL is therefore more a collaboration agreement between Italian mathematics as a whole and French mathematics as a whole. What are the themes at the heart of this already very active cooperation?

G. P. : The Ypatia Laboratory aims is to facilitate scientific exchanges between France and Italy in all branches of mathematics. It builds on previous experiences and a strong track record of successful collaborations in a variety of different topics, ranging from algebraic and complex differential geometry to non-commutative geometry4 , number theory, analysis in the broad sense, mathematical physics, statistical mechanics, ergodic theory and dynamic systems5 , probability and interacting particle systems, and logic. Though this is a long list, it does not cover all possibilities. The goal is to consolidate existing successful collaborations, and to create new ones in other areas of contemporary interest for French and Italian mathematicians.

What is the international standing of Italian mathematics?

G. P. : The areas that I pointed out as being of core—but not exclusive—interest to the LYSM Laboratory are good examples of topics in which the Italian mathematical community has a long-standing tradition, and can celebrate many important achievements. We can also be proud of the contributions of our recognized international champions, such as the Italian Fields medal winners Enrico Bombieri (1974) and Alessio Figalli (2018), whose fundamental work embraces many important areas of mathematics that were and remain important in Italy. Yet instead of citing contributions, I think what is most significant is the degree of integration within the international scientific community, and being attuned to its most significant goals. In this regard, I believe that Italian mathematics is very healthy, and performs very well.

• 4In mathematics, a binary operation is commutative if changing the order of the operands does not change the result, and is otherwise non-commutative.
• 5Ergodic theory studies the statistical properties of deterministic dynamical systems, which is to say systems with no random perturbations, noise, etc.

Mathematics has a considerable social and GDP impact. This fact is sometimes overlooked, especially in France. Is it well recognized in Italy?

G. P. : It is most unfortunate that the fundamental role of mathematics in economic and social development is not adequately recognized. Italy is no better at this than France or, for that matter, much of Europe. It is a key challenge for our scientific communities to raise awareness about the role of mathematics and the possibilities it can offer. It is of course a necessity for advancing mathematics, but is first and foremost a fundamental contribution for the progress of society. For instance, the Sustainable Development Goals of the 2030 Agenda are not realistic without a significant involvement of the mathematical sciences, and the full use of their impact. Another example of significant contemporary interest is the growing role of artificial intelligence (AI) in the most diverse fields: it requires refined mathematical tools to acquire robustness, and perhaps most importantly to make the mechanisms that characterize it sustainable, open, and fully understandable. This can help return control over AI techniques to users and society, thereby avoiding its potential darker aspects. Finally, it is a fact that everyday decision-making would greatly benefit from the enhanced understanding provided by mathematical information. The often-imprecise use of data in the COVID pandemic crisis, both in the news and in policy decisions, represents a recent and worrisome example that illustrates how much improvement is needed.

As in France, children’s level in mathematics (measured in particular by the PISA and TIMSS surveys) does not reflect the research carried out in the country. How do you explain this, and how can mathematicians help?

G. P. : The standard of mathematical education is another reason for concern. While there is no doubt that a large number of young people have mathematical talent, we are witnessing a growing and concerning decrease in basic average mathematical performance. The phenomenon concerns the whole complex of scientific disciplines, and more generally the growth of critical and analytical skills. To intervene effectively, political decision-makers must be convinced that specific tools and dedicated investments are needed, in addition to more dedicated educators and experts. It is also essential that the professional mathematical community find ways to collaborate with and make mathematical knowledge more accessible to a wider audience. This calls for enhancements to our pedagogy and communication. The community of physicists and life scientists seems to be much more aware of this question, and more effective, providing guidance on what can be done. Last but not least, a special effort is also needed in our community to enhance the mathematical talent of girls. We cannot move forward without removing every obstacle holding back the talent of half of all young people.