A 42-minute lecture by Andreas Läuchli exploring thermalization dynamics in closed quantum many-body systems with emphasis on precision large-scale analysis. Delivered as part of the Thematic Programme on "Entanglement in Many-body Quantum Matter: Dynamics, Dissipation, Equilibration" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Gain insights into how quantum systems reach thermal equilibrium and the mathematical frameworks used to analyze these complex physical phenomena during this specialized physics presentation scheduled for the May-June 2025 programme.