Configurations Spaces of Particles - Homological Solid, Liquid, and Gas
Explore the fascinating world of configuration spaces in this lecture on "Configurations spaces of particles: homological solid, liquid, and gas." Delve into the topology of configuration spaces of points in the plane and discover how this concept evolves when points are replaced by particles with positive thickness contained within boundaries. Investigate the mathematical implications of this generalization and its relevance to physics, particularly in understanding hard-spheres systems and their phase transitions. Learn how these configuration spaces relate to physicists' concepts of "phase space" or "energy landscape" for hard-spheres systems. Gain insights into the potential topological underpinnings of phase transitions, such as water changing into ice, and explore the current state of knowledge in this intriguing area of study.