The interaction of matter with radiation, whether photons or electrons, is a fundamental experimental approach for studying materials. It allows us not only to understand their intrinsic properties, but also to tailor new functionalities for technological applications.

Experimental spectroscopies such as photoemission, optical absorption, X-ray scattering, electron energy loss, transient absorption, and the use of intense laser fields, all probe electronic excitations. While density-functional theory (DFT)—the standard model in condensed matter physics—can accurately describe ground-state properties such as atomic structure, total energies, electronic density, and phonon modes, it falls short in capturing electronic excitations and excited-state phenomena. To overcome these limitations, we must go beyond DFT.

In recent decades, advanced ab initio methods capable of addressing excited states and spectroscopic properties have emerged and are increasingly used: Time-Dependent Density-Functional Theory (TDDFT) and Many-Body Perturbation Theory (MBPT), including Green’s function methods such as the GW approximation, Bethe-Salpeter Equation (BSE), and non-equilibrium Green’s function approaches.

Accompanying this theoretical development, a rich ecosystem of ab initio codes and algorithms has been created, allowing researchers to compute spectra and excited-state properties of realistic materials.

More recently, a new and timely player has entered the field: machine learning. Although this school focuses on the theoretical foundations of TDDFT and Green’s functions theory, we also aim to provide a timely overview of state-of-the-art machine learning techniques for electronic spectroscopy, covering both valence and core-level spectra.

This school offers a unique opportunity to explore the theoretical and numerical foundations of TDDFT, MBPT, and GF approaches, extending to modern topics such as high-throughput workflows and machine learning in spectroscopy.

Importantly, this is also a hands-on, practical school: all theoretical lectures will be complemented by computational sessions using state-of-the-art ab initio codes (ABINIT, DP, 2Light, EXC), applied to real materials.

Building on the success of previous editions, this school introduces several important novelties, inspired by the most recent and promising trends in theoretical spectroscopy:

• Machine Learning for Spectroscopy
  Machine learning has rapidly emerged as a transformative tool, not only for predicting total energies and material structures, but increasingly for spectroscopic observables. Spectra pose a unique challenge: unlike scalar quantities, they are frequency-dependent functions, making their prediction significantly more complex.
  In the previous edition of the school, the DFT course was expanded to include high-throughput computations. This year, we take a significant step forward by incorporating state-of-the-art machine learning approaches for the prediction and interpretation of spectra and dynamical features of materials.

• X-ray Spectroscopy and Core-Level Excitations
  While TDDFT and MBPT have traditionally focused on valence excitations—drawing from their conceptual roots in the homogeneous electron gas—recent years have seen a surge in core-level spectroscopy applications. This shift is driven by dramatic improvements in experimental techniques available at modern synchrotron radiation facilities, which are now capable of probing electron excitations with unprecedented resolution, especially in scattering conditions.
  To meet the growing demand for accurate theoretical modeling of these experiments, this edition introduces a dedicated session on X-ray spectroscopies, including both absorption and scattering techniques. Special focus will be given to Resonant Inelastic X-ray Scattering (RIXS), one of the experimental methods that has benefited the most from recent advances in instrumentation, and that poses particularly rich and challenging questions for theory.

• Workflows and automating
  Another important novelty of this edition of the school—this time on the more practical and technical side—is the introduction of workflows to automate complex sequences of calculations that precede excited-state simulations. Before reaching the stage of TDDFT or MBPT calculations, several ground-state steps  are typically performed: structural relaxation, convergence tests on k-points and energy cutoffs, ground-state calculations for the electron density, and preparation of input data for excited-state codes. These tasks are not only time-consuming, but also prone to user errors when performed manually. This year, we will introduce modern workflow engines and demonstrate how they can streamline and automate these multi-step procedures, improving both efficiency and reproducibility. Students will gain hands-on experience with such tools, learning how to build robust pipelines for ab initio spectroscopic simulations.

Finally, it is important to highlight that the hybrid format has proven valuable and highly appreciated even beyond the duration of the school. We recorded the lectures from the previous edition and made them available as a YouTube playlist (https://www.youtube.com/playlist?list=PLD59gCifE4d_hgsmxFrEiU58n3rdiDGDi), which has now collected over a thousand views. This extended the reach of the school to a broader audience of young researchers, including those who could not attend in person.