Clara Torres has received the 2025 Vicent Caselles Award for the “exceptional significance” of her work during her PhD. Image courtesy of the researcher

Laura M. Iraola (ICMAT-CSIC)

The BBVA Foundation and RSME’s Vicent Caselles Award is a recognition of your doctoral work. Could you explain what it consisted of?

My thesis focused on various problems in what’s known as regularity theory, a branch of partial differential equations that seeks to understand when the solutions to these equations are smooth and when they have singularities. That is, if an equation describes how a certain physical quantity – depending on space and time – evolves, why does that quantity sometimes blow up – take infinite values – and sometimes not?

And why is that relevant?

For instance, to assess whether physical models are accurate or not, but also to describe new phenomena such as black holes.

What were the specific results of your work?

One physical model I worked on describes how a piece of solid, like ice, melts into liquid. In my thesis, I obtained estimates on how the solutions behave and what shape they take near the boundary separating the liquid from the solid, and near the edge of the container holding both.

How did you start working on these types of problems?

As has happened to many others, it was thanks to the influence of a teacher, Alejandro Miralles, from the University of Valencia. During secondary school, I took part in the ESTALMAT Valencia programme, an initiative to nurture mathematical talent in young students. I used to approach the teachers there and share my questions. Miralles, in particular, was very engaged with me, and since he specialised in analysis, he would tell me about problems in that area. By the time I got to university, I had almost completed the syllabus for the analysis branch of the first two years. So, continuing in that direction was a natural step for me. It’s something I had practically been doing since I was twelve. Also, when you’re good at something, you tend to enjoy it.

What were your PhD years like?

The hardest part was starting the thesis without knowing anyone, during the COVID era. I couldn’t go to university or pursue my hobbies, so that first year of the PhD wasn’t great. On the other hand, there were also really lovely moments and I connected with many people on a personal level. In fact, I created a WhatsApp group with the people doing their PhDs at the University of Barcelona. I acted as the glue and organised social activities, like a board game day or a discussion evening, with pizza, around a video.

“By the time I got to university, I had almost completed the syllabus for the analysis branch of the first two years”

You joined ICMAT as a postdoctoral researcher at the end of 2024. What are you working on now?

My main project at the moment deals with the Euler equation, which describes the motion of incompressible fluids without viscosity, in two dimensions. Specifically, we’re trying to find examples of solutions with very particular features. I’m working with Alberto Enciso, the head of my group at ICMAT, and also with Antonio J. Fernández from the Autonomous University of Madrid.

What do you like most about research?

The excitement of understanding something I didn’t understand before.

“I do research for the excitement of understanding something I didn’t understand before”

When did you start liking mathematics?

I think I’ve liked it all my life. It’s curious, because no one in my family works in mathematics. The first time I remember thinking about studying a degree in Mathematics I must have been about seven, but even at five I remember playing with the typical foam mat with puzzle-like pieces and looking at when I could pick up a rectangle and rearrange the pieces to make a square, and things like that.

What milestone would you like to achieve as a mathematician?

I’d like to contribute something of value to society and give back everything I’ve received during my educational and research career, so I’d like to do something that makes sense to others. At the moment I’m advising a group that works on ethics and evaluation of artificial intelligence in areas related to mathematics, and I plan to explore other paths in that direction.

Who are your role models?

In the field of mathematics, Alejandro Miralles and Xavier Ros Oton – my former teacher and PhD supervisor, respectively. Outside mathematics, Alok Kanojia (Dr K), a psychiatrist and YouTuber specialising in mental health. He helped more than one of us a lot during lockdown.

What do you like to do in your free time?

Mainly music – I sing in a choir and also play keyboard in a band. I also enjoy reading; lately, I’ve been leaning more towards the social sciences.

“I want to do something that makes sense to others”

Is there a book, film or album you’d recommend?

I recommend Moral Ambition by Rutger Bregman. It’s a book that explores the lives of people who have changed society in some way because they looked beyond themselves. It makes you reflect on whether those of us in some position of privilege could be doing more.