While electrons in disordered systems have been studied early on leading to the Nobel prize in physics 1977 for Phil W. Anderson and Sir Neville Mott, a similar understanding of phonons and lattice dynamics of disordered and amorphous systems, or systems with strong anharmonicity, is still at its infancy. This field is currently blossoming due to its centrality in contemporary condensed matter physics and materials physics. In particular, to arrive at a deeper understanding of complex materials (e.g. polymers, metallic glasses, high-T superconductors) it is essential to develop a successful description of vibrational modes, soft modes and elasticity/mechanical instabilities in these systems [1-4]. I will briefly review our new understanding of phonons and elasticity in real complex solids, including polymers, from the angle of my recent contributions to the field. In the second part, I will show how this understanding can lead to a theoretical framework which describes and rationalizes superconductivity in disordered systems such as metallic glasses  and high-T superconductors at high pressures, which have currently achieved record high Tc at room temperature [6-7], and where anharmonicity plays a crucial role.
 A. Zaccone and E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011)
 M. Baggioli and A. Zaccone, Phys. Rev. Lett. 122, 145501 (2019)
 M. Baggioli and A. Zaccone, Phys. Rev. Research 2, 013267 (2020)
 A. Zaccone and K. Trachenko, PNAS 117, 19653 (2020)
 M. Baggioli, C. Setty and A. Zaccone, Phys. Rev. B 101, 214502 (2020)
 C. Setty, M. Baggioli and A. Zaccone, Phys. Rev. B 102, 174506 (2020)
 C. Setty, M. Baggioli and A. Zaccone, arXiv:2007.04981
Born in 1981, after a PhD at ETH Zurich (during which he developed the extension of the DLVO theory of colloidal stability to systems in shear flows, in Zaccone, Wu, Gentili et al. 2009), he has been on the faculty at Technical University Munich, University of Cambridge and, currently, at the University of Milan. He made contributions to the lattice dynamics, elasticity and viscoelasticity of liquids and amorphous solids, including the microscopic mathematical theory of elasticity of random sphere packings and elastic random networks (Zaccone & Scossa-Romano 2011), and a popular model for the elasticity of colloidal gels/glasses (Zaccone, Wu, Del Gado 2009). He also developed what is now sometimes being referred to as the Krausser-Samwer-Zaccone (KSZ) model for the viscosity of liquids (Krausser, Samwer, Zaccone 2015) and, with E. Terentjev, a molecular theory of the glass transition based on thermoelasticity and disorder-assisted Born melting (Zaccone & Terentjev 2013). More recently, with K. Trachenko, he predicted that the low-frequency shear modulus of confined liquids (under good wetting conditions) scales with the confinement length to the power of minus three, a new law that has been observed experimentally in many different systems. With M. Baggioli he predicted that the “glassy” boson peak in the Raman and neutron scattering DOS spectra of solids is actually a more general feature arising from anharmonicity, which explains many recent experimental observations of boson peak in ordered crystals (Baggioli & Zaccone 2019). In recent work with C. Setty and M. Baggioli, he has developed a more general theory of boson-mediated superconductivity which extends the Eliashberg/BCS theory to real materials with strong anharmonicity, and/or structural disorder, and to high-pressure systems, with the aim of better understanding superconductivity in complex systems, including the new generation of room-temperature high-T/high-P superconductors.