Every March, a few hundred secondary school students take over a conference hall in Barcelona to explain their research projects to anyone willing to stop at their stand. The projects range widely: genetics, climate, sociology, and engineering. This year, the Centre de Recerca Matemàtica sent five people to look for mathematics in the mix.

It was CRM’s third time at Exporecerca Jove, the international research fair for students aged 12 to 19, organised by MAGMA. The institute has been a sponsor since the fair’s XXVII edition and awards a prize to the project with the strongest mathematical content: an invitation to participate in one of the scientific activities held at CRM.

After reviewing seven projects on 6 March, the jury selected two winners.

The first was Xavier Ortiz Quintana, a student at INS Montserrat Roig. His project reconstructed 3D models of real spaces in real time, using only a standard iPhone and a laptop. The setup sounds simple. The algorithm underneath is not. Depth data captured by the phone’s LiDAR sensor is integrated, frame by frame, into a mathematical structure called a Truncated Signed Distance Field. The TSDF is a volumetric representation that stores, for each point in a grid, a signed number: positive if the point is outside a surface, negative if it’s inside. The boundary where that number crosses zero is the surface itself. An algorithm called Marching Cubes then reads that grid and constructs a mesh of triangles that approximates the shape. It’s a technique from 1987, originally designed for medical imaging, here running on a GPU in a teenager’s bedroom. Xavier has published the full code on GitHub.

The second winner was Bruna Basas Jaumandreu, from La Salle Manresa, who trained a machine learning model to predict whether a pancreatic cancer patient would survive beyond 24 months after diagnosis. Pancreatic cancer is one of the deadliest: only about 13 per cent of patients survive five years. Part of the difficulty is late detection; another is that treatments work unevenly across patients. Bruna’s logistic regression model, built on clinical and mutational data from 2,336 patients and developed in collaboration with the Institute for Biomedical Research of Barcelona, reached 74.1 per cent accuracy. The variable that most increased survival probability was the surgical removal of the tumour. The one that most reduced it was age over 90. Both results are consistent with published studies, which is the kind of confirmation you want when working with a 185-patient validation cohort.

The jury walked the stands on a Friday morning in early March: Javier Guillán (PhD student), Ander Movilla (Beatriu de Pinós postdoctoral fellow), David Romero (director of the Knowledge Transfer Unit), and Pau Varela and Natalia Vallina from the Communications and Outreach team.

CRM’s prize is not a certificate. It is access: a place at one of the institute’s research days, seminars, or outreach events, where the winners will be in the room with working mathematicians. What they do with that is up to them.