| Abstract: Galaxies lie at the nexus of modern astrophysics—serving as essential cosmological probes, while setting the environment in which stars form and compact objects merge. Yet, despite their central role, the physics governing their evolution remains elusive. The key lies in deciphering the intricate balance between inflows and outflows that shape galaxies and regulate the fuel supply for star formation and black hole growth. In this talk, I will describe my efforts to forge a robust framework that self-consistently captures the governing processes across a daunting range of scales by combining state-of-the-art simulations, intuitive analytic models, and novel numerical methods. I will show how micro-scale (~sub-pc) processes, such as cosmic ray transport, magnetic reconnection, and turbulent mixing, connect with meso-scale (~kpc) phenomena, such as supernova-driven galactic winds, and how—when combined using innovative multi-scale techniques—they shape the macro-scale (~Mpc) dynamics and galactic properties. This approach bridges not only scales but also diverse disciplines—from fluid dynamics and plasma physics to cosmology, with insights drawn from climate modeling and pure mathematics. Taken together, these efforts aim to reshape our interpretation of observations and usher in a new era of truly predictive galaxy modeling built on a foundation of solid physical principles. |