MSCA-SE.26.Roncal

Objective:

This project addresses the growing need for advanced analytical tools capable of handling complex, high-dimensional and non-Euclidean data arising in contemporary science and technology. Fourier analysis has long played a central role in mathematics and its applications, particularly in partial differential equations (PDEs) and signal processing. Recent developments in graph-based models and machine learning, however, call for new theoretical frameworks extending classical Fourier methods beyond Euclidean settings. It aims to develop and integrate emerging Fourier-analytic techniques for graphs, machine learning and PDEs, establishing a unifying perspective that connects harmonic analysis, spectral theory, time-frequency methods and data-driven approaches. The research programme focuses on Fourier analysis on graphs and networks, spectral and microlocal methods for evolution PDEs, and Fourier-based interpretations of learning models, with particular attention to stability, representation and generalization. The action is implemented through an international and intersectoral consortium of academic and non-academic partners. Staff exchanges constitute the core mechanism to foster knowledge transfer, enabling researchers to operate across disciplines and sectors while addressing both theoretical and application-driven challenges. Through mobility, joint research activities and networking events, the project strengthens long-term collaboration, enhances the research and innovation capacity of the participating organisations, and contributes to the training and career development of staff members. By advancing foundational mathematics while promoting its transfer to machine learning and graph-based applications, the project contributes to scientific excellence and supports the development of innovative analytical tools relevant to modern data science and applied mathematics.