Supporting New Collaborations in Mathematics

Cristina Trombetti is the president of INdAM, the Italian National Institute of High Mathematics, which partners with ICTP to support the Research in Pairs programme, promoting collaborations between mathematicians in developing countries and INdAM members.

Trombetti is a mathematician specializing in partial differential equations. After a degree and a PhD in mathematics at the University of Naples Federico II, Trombetti continued her career there as a researcher and professor. Recently, she chaired the mathematics department for six years, until December 2024. She has been the president of INdAM since January 2024. “It has been a great experience,” she explains, adding, “INdAM is an active and vibrant institute, thanks to the work of many people who are fond of the discipline and believe in the power of collaboration.”

As ICTP and INdAM are working to renew and expand their partnership, Trombetti agreed to be interviewed about the Research in Pairs programme that the two institutes have organised together since 2014.

What is INdAM’s mission?

INdAM has a dual mission of supporting research in mathematics and training new generations of mathematicians. To do that, it sponsors schools and summer courses for students at all stages of their training, from undergraduate to PhD. It also awards scholarships for undergraduates and early career researchers.

Within INdAM there are four distinct research areas: mathematical analysis, probability and their applications; algebraic and geometric structures and their applications; mathematical physics; and scientific computing.

Almost all active researchers in mathematics in Italy are INdAM members. They can apply to take part in the projects we organise, often in partnership with other institutes, both in Italy and abroad. Our partners include the Italian Mathematical Union, the Italian Society of Applied and Industrial Mathematics, the ERCOM (European Research Centres on Mathematics), the French National Council for Scientific Research, the International Mathematical Union, and of course ICTP.

How does the partnership with ICTP help you carry forward your mission?

Joining forces with ICTP has been crucial to fostering research collaborations in mathematics, particularly with international researchers. The initiative we support together is particularly important because research in pairs is extremely formative for researchers.

Why is collaboration, and particularly international collaboration, so important in your view?

Research is about breaking new ground and exploring new aspects of knowledge. It requires original ideas and an awareness of what is going on in other research groups around the world. Discussions and exchanges are one of the most important factors in fostering new ideas and new avenues of research, which is why INdAM promotes various types of collaborations that stimulate joint research projects between researchers from different countries.

What is the specificity of research in pairs, and why do you consider it so important?

Research in pairs is a unique and worthwhile experience, especially if done early in one’s career. Working with people we do not know requires flexibility and the capacity to adapt one’s thinking and working style in order to team up constructively with someone else. This form of collaboration is an excellent encouragement to do that because it creates the conditions for two people to spend extended time together, in an environment where they can focus solely on their joint research. This is critical, since in a usual workday we are continuously distracted by many tasks that take us away from our research topic. Moving to another institute or even country to start a new collaboration gives one the opportunity to immerse oneself in another world, which can spark new ideas.

What are your hopes for the partnership between INdAM and ICTP?

We started collaborating in 2014 and have renewed our partnership on the research in pairs initiative regularly since. Having reached the 10-year milestone, we are excited to enter a new phase in our joint effort. We intend to continue to support the research in pairs programme, which is a flagship. Recently, we have applied together to the Simons Laufer Mathematical Sciences Institute (SLMSI) for the possibility to organise a summer school there on topics related to machine learning and artificial intelligence, which is planned for 2026. We hope that our project will be accepted!

In June 2025 ICTP was pleased to welcome a cohort of 11 researchers from Italy and around the world, who have come to Trieste to carry out their research projects in pairs. Bringing together researchers from Italy and from countries as varied as Brazil, Algeria, and Argentina, the pairs—or triplets—supported by the ICTP-INdAM partnerships this year will benefit from the opportunity to focus on their research undisturbed and to take full advantage of the ICTP campus facilities.

Highlights from the projects completed earlier this year by the 2024 cohort are featured in this article, offering a perspective of the initiative’s reach and impact.