Renormalization group theory provides a framework for understanding critical phenomena and phase transitions. It helps explain universality, where physically different systems share patterns of behavior near a critical point.
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43:08Hbert's 10th problem 1971 renormalization group theory. Yes, this is um near and dear to me. This is in statistical mechanics. Theoretical physicist Kenneth Wilson formulated the renormalization group theory at Cornell University and he provided a mathematical framework to analyze critical phenomenon and phase transitions. This is the stuff of how magnets work at low temperatures or um how gases and liquids behave at that critical point. It turns out there's something called universality. Meaning um gases of any type, if you look at how they behave in at the critical point when they have this critical phenomenon,
43:49they all behave exactly the same regardless of the constituents of the material. um he proved some very deep things about like it matters the dimensionality of your parameter. For example, if the parameter you're keeping track of is temperature, that's a one-dimensional parameter. It can either go up or down. But if you're keeping track of let's say magnetic spin, spin is a three-dimensional parameter. And that number is what matters. So it doesn't matter if you're keeping track of like whatever thing. It's how many numbers are you using it to describe that thing. It's so deep and it's one of my favorite courses that I ever took at at grad school was statistical field theory where we went over reormalization group theory. It also has um deep
44:32impacts to quantum field theory because you know we talk about the infinities that come up in quantum field theory. Well, reormalization is actually how you resolve them. >> Kenneth Wilson discovered all of that. 1982 Nobel Prize in Physics.