# Interdisciplinary reorganization of mathematics thematic networks

Earth and energy, algebra, geometry, health, didactics, history, probability, analysis, statistics, arithmetic, optimization... These are just some of the disciplines covered by the 16 new thematic networks of the Institut national des sciences mathématiques et de leurs interactions (Insmi), to be set up in 2024.

Thematic networks (RT), or research groupings, are structures for scientific coordination on a national scale. In 2024, they were reorganized around fifteen major research themes.

Get an inside look at this reorganization with the testimonials of four RT managers: Boris Adamczewski, Isabelle Chalendar, Olivier Dudas et Chi Tran.

### A wide range of research topics

In 2024, the research networks were reorganized by grouping together two or three similar research themes. The number of networks has been reduced from 29 to 16. These networks animate and federate the mathematical community, stimulate interaction between mathematicians and encourage interdisciplinarity. The topics covered by the thematic networks are wide and varied: earth and energy, algebra, geometry, health, didactics, history, probability, analysis, statistics, arithmetic, optimization... Find the full list **here**.

Olivier Dudas, head of the Algebra network (ALGBR), points out that “*algebra is an extremely vast field*”. As such, the ALGBR network “*cannot claim to bring together all algebraists in France, but rather to support certain communities around strong or emerging algebra-related themes*”, he adds.

Within these networks, research axes have been established to blend the issues of the former GDRs at the origin of each network. According to Boris Adamczewski, head of the Number theory (RT2N) network, “*The network's structure is set to endure, as the field is stable. On the other hand, the lines of research may vary according to the connections between researchers. These axes will also encourage exchanges with other networks, which may be mathematics networks or other institutes*”.

Among these 16 networks, the Mathematics of Randomness for Risk (MATRISK) network is new on the scene. This network is headed by Anis Matoussi and Chi Tran. Chi Tran sums up the genesis of the project: “*We had contacted Insmi back in 2022, but as the RTs were being restructured, we had to wait for our thematic network to be created. However, this allowed us to fine-tune our project. Starting with an initial proposal based on actuarial mathematics, we have built a thematic network that today brings together four areas: actuarial mathematics, financial mathematics, probability and risk statistics, and rough trajectories. These mathematical specialties work and develop in synergy*”.

**I**nterdisciplinarity at the heart of thematic networks

Interdisciplinarity is at the heart of the thinking behind this reorganization. “*We know the extent to which the meeting of two mathematical fields leads to unsuspected discoveries, and we want the Algebra thematic network to play this role*,” notes Olivier Dudas. In the same spirit, Chi Tran, head of the MATRISK network, is enthusiastic: “*It's going to be exciting to get mathematicians from different schools working together on these issues*”.

These thematic networks are made up of former research groups whose research themes were similar, but not identical. For Isabelle Chalendar, head of the Analysis and Interactions(ANAIS) network, “*several ANAIS network members already belonged to two former GDRs: Analyse Fonctionnelle, Harmonique et Probabilités (AFHP) and AMA. It was therefore only natural to bring them together*".

For others, the restructuring of the thematic networks will enable them to engage in exchanges that are sometimes unprecedented or less intense than hitherto. This is the case for RT2N, as Boris Adamczewski observes: “*For example, in terms of links with computer science, I'd like to see us find a slightly clearer structure. And then, the human aspect is important to take into account: certain themes tend to be more conducive to collective work. The thematic axes will never cover all the parts of number theory represented in France, but they do reflect the way the field is structured*”.

**What are your medium-term objectives?**

Within the ANAIS network, the team's first priority is to consolidate internal scientific links, and to this end it is organizing a conference entitled *Les premières rencontres d'ANAIS*, from November 04 to 07, 2024 at the Gustave Eiffel University. “*The steering committee met by videoconference in January, and we have invited six speakers to cover as many research topics from our vast network as possible. Most of them are very promising young scientists, some of them post-doctoral fellows or newly-qualified researchers*", adds Isabelle Chalendar.

In the same vein, the MATRISK network aims to “*create a framework for exchanges that will encourage the emergence of new mathematics and new projects, on subjects touching on the transitions in our societies. This national network will also raise the profile of these issues among both academics and companies*", confirms Chi Tran.

The delimitation of certain former research groups within the same thematic network is sometimes still very visible, and this can be felt within the teams. For Olivier Dudas, “*one of our network's first goals will therefore be to facilitate encounters between the two communities, notably by organizing joint events (the first of which took place in mid-March) so that each can benefit from the other's expertise*”.

Boris Adamczewski notes that “*it's going to be interesting to work on meshing and connecting the networks. For the moment, we're just structuring our own network. Everything in its own time*”.

**Restructuring initially met with a lukewarm reception**

How was the restructuring received? "*With a bit of mistrust at first, as is often the case with change*", comments Olivier Dudas. Indeed, the changes initially caused concern within the scientific community, “*not entirely convinced by this restructuring, which doubled the size of our research group*”, notes Isabelle Chalendar. Boris Adamczewski agrees, noting that “*colleagues initially thought that the research groups would come to an end, or feared that what would follow would not be as good. We found out about the allocated budgets relatively late. Some colleagues were also nervous about being grouped together with non-specialists in number theory*”.

But in the end, “*The organization of this thematic network and its implementation came about very naturally, given the scientific links that already existed*”, says Isabelle Chalendar. “*We can understand the tension surrounding these names,*” adds Olivier Dudas, “*but in practice, the construction of these networks should help to break down barriers*". Boris Adamczewski, for his part, is rather optimistic: “*Efforts have been made to ensure that, in the end, everyone can find their way around. What we've seen so far is that in the first year, the resources we've been given to operate are sufficient. We can operate with equivalent resources, while creating new things like this new arithmetic geometry axis*”.

The MATRISK network has been enthusiastically welcomed as a new theme in which statistics can be represented. According to Chi Tran, “*University research on some of the topics covered by the RT is scattered across the country, and lacks scope in France. Many young people trained in these areas move on to the private sector, where R&D is sometimes very active. The creation of the network is therefore something that we academics are delighted about, and will give our community dynamism and visibility*".

**Steps for young colleagues**

Actions aimed at young mathematicians are one of the priorities of the thematic networks. This includes the inclusion of these young colleagues, for example at annual meetings where the ANAIS thematic network encourages them to present their work. “*This enables the community to get to know the candidates for research associate, lecturer or post-doctoral positions. We organize spring schools to consolidate their scientific background as much as possible, but also to create synergy between young researchers,*” argues Isabelle Chalendar. Olivier Dudas also supports this approach, as it “*enables the youngest members of the network to share their work (recent or future) with the algebra community, giving them special consideration for future recruitment or promotion*”.

For Olivier Dudas, the first action of the ALGBR network will be financial support: “*Although our young members are often the most active, they are also those who have the least means to finance their missions (scientific visits, conferences...) and their invitations. Part of the budget is dedicated to them, and special attention is given to them when the RT financially supports a scientific event*”. The MATRISK network is also planning to provide support in this area, in order to “*shed more light on these forward-looking subjects, linked to the mathematics of randomness for risk, making it more attractive to young people and enhancing the value of future research among peers and companies*”, says Chi Tran.

Boris Adamczewski estime qu’un RT est « *d’abord un lieu d’information. Le RT2N va relayer des annonces de conférences, de postes, post-doc… ce sont des choses très importantes, surtout pour les jeunes* ». Selon lui, il est important de fédérer les membres du réseau afin de susciter un « *certain degré d’appartenance et de communauté. *». Il est tout autant important de pouvoir identifier des personnes en dehors de son domaine de recherche précis, car « *il est illusoire de penser qu’être vraiment ultra spécialiste de son problème c’est la bonne façon de le résoudre, il faut souvent aller piocher ailleurs* ».

Boris Adamczewski believes that an thematic nework is “*first and foremost a place for information. The RT2N network will relay announcements of conferences, positions, post-docs... these are very important things, especially for young people*”. In his opinion, it's important to unite the network's members to create “*a certain sense of belonging and community*”. It's just as important to be able to identify people outside one's own specific field of research, because “*it's an illusion to think that being an ultra-specialist is the right way to solve a problem*".

### Find out more about the thematic network managers' day

CNRS Mathematics is organizing a day dedicated to thematic network managers on Wednesday, November 06, 2024 at the Centre de Recherche en Mathématiques de la Décision (CEREMAD), Paris (France).