Courses 2026-2027

Scanning Probe Microscopy (SPM) represents one of the most powerful tools for scientific research, able to generate maps of surfaces with atomic/nanometric resolution. SPM represents a big family of different techniques: Scanning Tunneling Microscopy, Atomic Force Microscopy, Magnetic Force Microscopy, Friction Force Microscopy, etc. Depending on the sensitive quantity (tunnelling current, magnetic force, friction force, etc), the generated maps give information about many different properties of the surfaces. For these reasons, SPM is used in many scientific fields and on very different systems, including inorganic solids, polymers, biological systems, etc. In this course the main principles and characteristics of SPM will be delivered, together with some case studies.

• Principles and applications of widefield, confocal microscopy, and optical nanoscopy.
• Principles and applications of probe microscopies for cell and biomolecular characterizations.
• Principles of electron microscopy and applications on biomolecular characterization.
• Selected concepts and examples in image processing for microscopy.
• Selected non-imaging methods for the characterization of nanoscale structures of biological interest (FCS, DLS, nanopore techniques, NTA, cytofluorimetry, …)

– General scattering theory (2h)
– Sources and experimental perspective on instruments (2h)
– Resonant Scattering and Diffraction (2h)
– Resonant Inelastic X-ray Scattering and excitations (2h)

Electron microscopes are often seen as machines that take high-resolution images of small objects. This course shows why that view is incomplete. A transmission electron microscope is a tunable scattering experiment: a high-energy electron beam interacts strongly with matter, and every detector, mode or spectrometer measures a different aspect of that interaction. The course is aimed at PhD students, from experimental or theoretical and computational backgrounds, and assumes no previous experience with electron microscopy. We start from the physics of electron-matter interaction and compare it with X-ray scattering, to understand where electrons are the right probe and where they are not.

We then follow the electron through the instrument, discussing sources, lenses, aberrations and detectors, and ask what limits resolution in practice.

The central part of the course covers the main ways of extracting information from the sample. Diffraction and TEM imaging link real and reciprocal space, and show why high-resolution images cannot always be read at face value. Scanning TEM adds probe-based imaging and compositional contrast. A full session is dedicated to spectroscopy, in particular electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray analysis, which provide access to composition, bonding and electronic structure, and which connect directly to ab initio calculations of dielectric response and core-level excitations. Sample preparation and beam damage are discussed throughout as limits on what a measurement can actually tell us.

The course closes with phase retrieval. Because detectors record only intensity, the phase of the electron wave is lost, yet it carries information on electrostatic and magnetic fields. We introduce off-axis electron holography and 4D-STEM methods, including differential phase contrast and ptychography, as two different strategies to recover it.

Short hands-on sessions based on Python notebooks, together with examples of comparing measured and simulated data, will help students judge what a given technique can and cannot tell them about their own samples.

– Introduction to electrochemical energy storage: batteries and capacitors. Interfacial capacitance: electrical double layer and potential of zero charge. Helmholtz, Gouy–Chapman and Stern models. The Poisson-Boltzmann (PB) model and solution. Beyond PB: ionic saturation and Fermi-Poisson model. The jellium electrode model and electronic effects. (3 hours)

– Theory of ionic screening: Debye-Hückel (DH) theory and screening lengths. Concentrated electrolytes and pathological underscreening effects. Elements of classical density functional theory. Beyond DH:  asymptotic expansion of the excess free energy. Screening crossover and Fisher-Widom line. (3 hours)

– Atomistic simulations: constant charge vs. constant potential. Classical representations: extended Largrangian Siepmann-Sprik model. Grand-canonical (electronic) density functional theory. Computing the electrode potential from simulations. Periodic boundary conditions and finite-field methods. (3 hours)

– Atomistic machine learning (ML) and breakdown of short-range models. Overview of long-range electrostatics in atomistic machine-learning. ML models for electrochemical interfaces and finite-field coupling. Towards electronic-structure ML models: learning the electron density. Closing remarks on current and future challenges. (3 hours)

1. Kohn–Sham (TD)DFT Origins of DFT; Kohn–Sham system; N- and v-representability; time-dependent KS equations; Dyson equation; linear-response and real-time TDDFT. Jupyter notebooks on: plane-wave basis sets, Bloch’s theorem, k-point sampling, Poisson solver, KS implementation in Quantum ESPRESSO; applications via ASE and QEpy. (4 hours)

2. Orbital-Free (TD)DFT Reference systems for OF-DFT; Boson KS system; Pauli energy functional; approximations to the Pauli potential; time-dependent OF-DFT. Comparing KS-DFT and OF-DFT in Jupyter notebooks using DFTpy; bulk Al/Si simulations; TD-OF-DFT for plasmonic response of nanoparticles. (4 hours)

3. (TD) Density Functional Embedding Theory DFET, Partition DFT, FDE, and projection-based embedding; OEP method; analysis of uniqueness; extensions to the time domain and linear-response embedding; connection to open-system physics. Adaptive embedding simulations using eDFTpy; student-selected systems (condensed-phase molecular systems, interfaces, etc.); data analysis and evaluation of embedding performance. (4 hours)

4. Quantum Machine Learning for Electronic Structure 1- and 2-RDM–based ML; learning electron densities, 1-RDMs, and 2-RDMs; Hohenberg–Kohn theorems in ML workflows; kernel ridge regression; size-extensivity, N-representability, and extrapolation behavior. Jupyter workflows using QMLearn: dataset generation, training ML models, deployment; MD simulations using ML-based electronic structure; applications to embedding workflows.( 4 hours)

A self-contained introductory course on applications of the gauge/gravity correspondence to quantum many-body systems and quantum matter, with a focus on holographic superconductors and superfluids, holographic strange metals and holographic chaos.

A self-contained introductory course on integrability approaches to many-body systems, such as the Heisenberg spin chain and electrons in a lattice. Some of the techniques introduced in the course are the algebraic Bethe Ansatz and the S-matrix bootstrap.

– Motivations. Topological currents. Derrick theorem. Mathematical preamble to topological notions. Topological and non-topological solitons. Korteg-de Vries equation. (6 hours)

-Kink Solutions (1+1 dim.) and Instantons (0+1 dim.): Spontaneous symmetry breaking in φ4 model and kinks. Stability. Quantization of the kink motion: center of mass, zero modes and collective coordinates. Connection to instantons in Quantum Mechanics and non-perturbative effects. (6 hours)

-Vortices (2+1 dim.): global and local U(1) vortices. Abelian Higgs model and AbrikosovNielsen-Olesen vortices. Bogomolnyi equations. (4 hours)

-Monopoles (3+1 dim.): Dirac monopole. ’t Hooft-Polyakov monopole in SO(3) Yang-Mills theory. (6 hours)

-Skyrmions (3+1 dim.): Skyrme field and its topology. Skyrmion solutions. (4 hours)

-Instantons (4+0 dim): Self-dual gauge field configurations. Zero modes. Yang-Mills degenerate vacuum and non-trivial gauge transformations. (6 hours)