Public conference as part of the Search for a professor in Theoretical physics.

Summary: Floquet engineering—the control of quantum systems through periodic driving—has emerged as a powerful approach to realizing novel quantum phases in solids. This talk begins with a conceptual introduction to the Floquet framework, highlighting effective Hamiltonians and quasienergy spectra. I will then present recent developments in photoinduced topological transitions and light-driven current generation in Dirac and Weyl materials. Finally, I will introduce the emerging platform of Dirac quasiparticles in surface acoustic wave (SAW) lattices, where dynamic band modulation enables control of topological states, analogous to cold atoms in optical lattices. This platform offers new possibilities for confining topological quasiparticles, inducing quantum anomalies, and enabling coherent quantum control through tailored phononic structures