Two CRM researchers begin their Marie Skłodowska-Curie fellowships

• Gustavo Ferreira and Tássio Naia, who joined the CRM in 2023 through the María de Maeztu programme, have started their Marie Skłodowska-Curie postdoctoral fellowships this September.

• Their projects explore key questions in complex dynamics and probabilistic combinatorics.

Two postdoctoral researchers at the Centre de Recerca Matemàtica (CRM), Gustavo Ferreira and Tássio Naia, began their Marie Skłodowska-Curie postdoctoral fellowships in September. Both joined the CRM in 2023 through the María de Maeztu Unit of Excellence programme and are now launching independent projects that explore the frontiers of complex dynamics and probabilistic combinatorics.

Gustavo Ferreira: understanding the unknown within complex dynamics

Ferreira’s project, HyCoWanDoCoDyn (Hyperbolic Components and Wandering Domains in Complex Dynamics), aims to shed light on one of the most intriguing questions in the field: what happens inside hyperbolic components when the systems under study are no longer of finite type.

“In dynamics, we like what’s called hyperbolic dynamics; these are the things we understand best,” he explains. “But when you move from finite to infinite type, the behaviour of the system changes a lot, and it’s not clear what’s going on inside the hyperbolic components themselves. Those bits that were so well understood before are now less clear. So the project is trying to make sense of what is going on inside these components.”

“The Marie Curie is a huge opportunity to bring together all the work I’ve done in bits and pieces and put it into a cohesive whole.”

His research connects two areas that have long puzzled mathematicians: hyperbolicity and wandering domains. “There are two big obstacles to understanding them in this new context, and they are bigger domains and wandering domains,” Ferreira says. “Wandering domains, in particular, are something I’ve worked on before, and we’re finally in a place where we can try to understand them in this context.”

After two short postdoctoral positions in the UK, Ferreira highlights the importance of having long-term support to consolidate a line of research: “The Marie Curie really is a huge chance to drive the nail home on this project. It’s the opportunity to bring together all the work I’ve done in bits and pieces in different places and put it all together into a cohesive whole.”

Ferreira has already been part of the CRM and Barcelona’s mathematical community for two years. “It’s been a huge plus, honestly,” he says. “There’s a very strong dynamics and analysis community here in Barcelona. There’s always someone to knock on the door and ask, ‘Hey, do you know anything about this?’ And even if you don’t find the help you need right now in Barcelona, there’s always someone coming for a conference or a research visit.”

Tássio Naia: rainbow structures and the power of probability

Naia’s project, PARTIORI (Rainbow partitions and oriented structures in random graphs), explores the intersection of combinatorial design theory, Ramsey theory, and probabilistic combinatorics. “I’m studying questions about ‘rich’ networks, whose connections are classified or oriented,” he explains. “In such networks one can ask whether they necessarily contain large substructures of a certain type, or whether it is possible to decompose the network’s connections into layers, each exhibiting a specific behaviour of interest.”

His research focuses on decompositions of coloured networks into a few “rainbow” substructures (paths or cycles) under different colouring regimes, and on the existence of large oriented structures in random graphs. “Recently, very powerful tools have been developed to address this kind of problem, combining algorithmic, algebraic and semirandom approaches,” he says. “While most research has focused on rigid decompositions, I’m adapting and developing these techniques toward a more flexible framework, hoping to obtain more detailed results by taking advantage of this extra room to manoeuvre.”

“It’s very rewarding to receive positive feedback on a research plan that you’ve been building over time.”

Naia views the Marie Skłodowska-Curie fellowship as both an opportunity and a motivation: “Besides funding my research, the fellowship provides a framework to develop other aspects of my professional training. I plan to make the most of it. It’s also very rewarding to receive positive feedback on a research plan that you’ve been building over time.”

Reflecting on his experience at the CRM and in Barcelona, Naia underlines the value of collaboration and exposure: “The last two years have been enriching in many ways. I’ve interacted with researchers from other areas, gained practical experience in organising meetings, classes, and courses, and even in drafting proposals and budgets for scientific events. It’s been a fantastic experience, and I’m glad to continue what I hope will be many more years working with the CRM team.”

The fellowships mark an important milestone for both researchers and the CRM itself, which continues to strengthen its international research community through the European funding schemes. As Ferreira and Naia begin the next stage of their careers, their work highlights the breadth and vitality of mathematics being done in Barcelona, from the intricate geometry of complex dynamics to the hidden order of random networks.