Advanced Mathematics: Bridging the Gap between Fundamental Theory and Real-World Impact

The Project

At the Centre for Mathematical Research (CRM), we recognize mathematics as the universal language that underpins many aspects of our world. It is a tool to explore everything from the mysteries of biological systems to the complexities of climate hazards, all through the lens of mathematics. Research in mathematics is about seeing the unseen and understanding how theories on paper help us overcome the challenges of the world around us.

This project invites you to explore the world of mathematics, where you will engage in research that spans a broad spectrum of topics. In particular, we want to offer two pathways for this: one exploring more theoretical topics of mathematics and one more focused on practical implementations of mathematical tools. The objective is to cover as much as possible the interests of every student, while equipping you with the necessary tools to approach and address critical issues ranging from ecological conservation to mobility optimization. We aspire to foster the interest in mathematics not only as a scientific field but also as a potential career, by demonstrating the pivotal role it plays in driving innovation and providing solutions to pressing global problems.

By participating in this project, you will contribute to cutting-edge research that has the potential to make significant real-world impacts. Now, how are we going to do this? This project is going to be hands-on and collaborative to the core. At CRM, you will have the opportunity to tackle both abstract and complex principles, while also experiencing how our research team is transferring them to real-world related issues by getting to know real projects we are working on. Here at CRM, we approach mathematics from a variety of angles, from neuroscience to genetics and evolution; from industrial solutions to algebra, homotopy theorygeometry and Partial Differential Equations; from natural hazards to dynamical systems.

The road won't always be easy. You will learn to work with data, build models from scratch, and test your ideas until they can be implemented. Think group brainstorming, work groups where problems are puzzles waiting to be solved, and discussions that open new worlds of understanding. By the end of this project, students won't just know math; they'll understand its heartbeat.

We hope that, after their stay with us, students see the world of mathematics differently. Mathematicians are thinkers, problem-solvers, and creators. This project is more than a learning experience, it's a doorway into a world where math doesn't just solve problems – it impacts our daily lives.

Sounds interesting? Welcome to the place where mathematics meets real-world challenges – and transforms them.

Matching profiles

This project would be particularly suitable for students with interests in the following areas:

  • Mathematics: Those with a passion for mathematical theories and their applications.
  • Physics: Students interested in the fundamental principles of the universe, where mathematical models often play a crucial role.
  • Engineering: Aspiring engineers who will benefit from understanding mathematical models and their applications in designing and problem-solving.
  • Environmental Sciences and Ecology: Individuals interested in understanding and modelling environmental systems and ecological interactions.
  • Biology and Evolutionary Biology: Those interested in the mathematical modelling of biological systems and evolutionary patterns.
  • Genetics and Biotechnology: Students keen on understanding genetic data analysis and the role of mathematics in biotechnological advancements.
  • Neuroscience: Individuals curious about the quantitative analysis of neural networks and brain functioning.

This project would appeal to students who are not only passionate about their respective fields but also keen on understanding the underlying mathematical principles that drive research and innovation in these areas.

Learning objectives
  • Use of various computer applications for analysis, numerical and symbolic calculus, graphic representation, and optimization, to experiment with and solve complex mathematical problems.
  • Develop the ability to analyze pertinent data in moderately complex real-life situations, propose and validate mathematical models using appropriate tools, and draw conclusive insights from the results.
  • Identify and appreciate the role of mathematics across various disciplines, understanding its integral presence and application in diverse fields.
Required materials


Coordinators of the project

Carlos d'Andrea

  • Full Professor at the Autonomous University of Barcelona (UAB) and affiliated researcher at the Centre for Mathematicl Research (CRM). Chief Editor of Collectanea Mathematica, and a member of the Editorial Board of the Journal of Symbolic Computation, Maple Transactions, Revista de Matemática de la Unión Matemática Argentina, and Revista de Educación de la Unión Matemática Argentina.
  • Member of the Advisory Council of the European lecture series on "Effective Methods in Algebraic Geometry" MEGA.
  • Principal investigator of the University of Barcelona node of the Marie Sklodowska-Curie H2020-MSCA-ITN-2019 Innovative Training Networks "GRAPE".

Natalia Castellana

  • Associate Professor at the UAB since 2010. She served as an EPSRC postdoc at Aberdeen University from 2000 to 2001, and she was a visiting professor at Purdue University in 2005.
  • Throughout her career, she has actively participated in numerous research programs and institutions, including the Mittag-Leffler Institute in 2006 and 2022, the Bernouilli Centre in 2005, the Max-Planck Institut für Mathematik in 2001 and 2022, the Fields Institute in 2020, the Banff International Research Centre in 2022, the Haussdorff Institute in 2022, ICTS Bangalore in 2023, as well as several workshops at the Matematisches Forschungsinstitut Oberwolfach. In 2012, she assumed the role of Coordinator for the Spanish Topology Network.
  • Her research primarily focuses on the exploration of homotopy properties within p-completed classifying spaces of compact Lie groups and fusion systems. She achieves this through the utilization of p-local group information, with a particular emphasis on maps between p-completed classifying spaces

Toni Guillamon

  • Associate Professor of Applied Mathematics at the Department of Mathematics of the Polytechnic University of Catalonia (UPC) and a researcher affiliated with the Centre for Mathematical Research (CRM). 
  • His research is based on a genuine immersion in neuroscience problems with the help of experimental experts, followed by the selection of appropriate mathematical tools to model and study specific problems. Currently, he is working on various issues in this interdisciplinary field, consistently developing computational methods, and using and analyzing mathematical tools.
Associated researchers

Kevin Martínez Añón

  • Predoctoral researcher at the Centre for Mathematical Research (CRM), working in the Mathematical and Computational Biology Group.
  • MSc in Advanced Mathematics from Polytechnic University of Catalonia (2019-2020); BSc in Physics and Mathematics from Oviedo University (2014-2019).
  • His research focus is on the mathematics of development and evolution.

Dídac Gil Rams

  • Bachelor's degree in Mathematics, majoring in fundamental mathematics, at Autonomous University of Barcelona (UAB) in 2019 and Master's in Advanced Mathematics and Mathematical Engineering at Polytechnic University of Catalonia (UPC) in 2020/2021.
  • Received a Santander-UPC research initiation grant (INIREC) during the Master's course, supervised by Inmaculada Baldomà and Pau Martín.
  • Began a PhD in dynamic systems within the Applied Mathematics program at UPC in the 2021/2022 academic year, with the same supervisors, focusing on studying the exponentially small splitting of semi-standard map separatrixes.

David Romero Sánchez

  • David Romero i Sánchez has a PhD in Mathematics from the Universitat Autònoma de Barcelona and is currently in charge of the Knowledge Transfer Unit of the Center for Mathematical Research.
  • His interests focus on dynamic systems and modelling, especially in the branches of numerical analysis, optimization and artificial intelligence applied, among others, to the world of transport.
The center

The Centre for Mathematical Research (CRM), founded in 1984, is Spain's oldest mathematics research institute.