Combinatorics | Renormalization group | Numerical analysis | Hopf algebras
In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field. It was , prompted by the work of Sylvester on change of variables in differential calculus, who first noted that the derivatives of a composition of functions can be conveniently expressed in terms of rooted trees and their combinatorics. pointed out that the Butcher group is the group of characters of the Hopf algebra of rooted trees that had arisen independently in their own work on renormalization in quantum field theory and Connes' work with Moscovici on local index theorems. This Hopf algebra, often called the Connes–Kreimer algebra, is essentially equivalent to the Butcher group, since its dual can be identified with the universal enveloping algebra of the Lie algebra of the Butcher group. As they commented: We regard Butcher’s work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results. (Wikipedia).
The Butcher: Mystery Meat | Exclusive | History
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The Butcher: Dave Cuts Steaks on the Bandsaw | Exclusive | History
Judge Dave gives viewers tips on how proper-sized steaks are trimmed on the bandsaw. #TheButcher Subscribe for more from The Butcher and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch full episodes on our site: http://po.st/the-butcher
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The Butcher: Sully Makes Sausages | Exclusive | History
Judge Sully goes through the process of making sausage from grind to stuffing. #TheButcher Subscribe for more from The Butcher and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch full episodes on our site: http://po.st/the-butcher Chec
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The Butcher: Roxanne Frenches a Rack | Exclusive | History
Judge Roxanne shows hows to french a rack of meat, from cutting the excess fat to cleaning the bones and tying it together. #TheButcher Subscribe for more from The Butcher and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about the show and watch full episode
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For millions of people, the word 'mafia' conjures images of "The Godfather" and "The Sopranos". But what is 'the Mafia', exactly? Where does the term come from, and how has the definition changed over time? SUBSCRIBE | http://bit.ly/stdwytk-sub WEBSITE | http://bit.ly/stdwytk-home AUD
From playlist Stuff They Don't Want You To Know, New Episodes!
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A quick definition of groups on the periodic table. Chem Fairy: Louise McCartney Director: Michael Harrison Written and Produced by Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation
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The Boys Season 2 SPOILERCAST - The Adam Savage Project - 9/29/20
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Danny Calegari: Big Mapping Class Groups - lecture 5
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The Butcher: Roxanne Grills the Perfect Steak | Exclusive | History
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Pig Out Panel 3: Pigs in the City
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