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Monthly Archives: February 2014
Wang Tiles – 1
In Penrose Tilings – 1 I introduced, briefly, Wang Tiles. I’ve been playing with them a bit since for a number of reasons. These tiles can represent a Turing machine and so a set of them represents a computer and a … Continue reading
Penrose Tilings – 1
I gave a “Pizza Pi” talk in my department this past Wednesday (2/19) on Penrose Tilings. It happened that back in December (’13) I had decided to start playing with Penrose Tilings, possibly to include it in a liberal arts … Continue reading
String Theory, Part V: Worldsheets and Currents
EDIT: It has been brought to my attention that I was getting ahead of myself a little bit. At this point let us elaborate on the concept of a worldsheet. We have been looking at worldlines which are the paths … Continue reading
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Lie groups and Lie algebras – 2
A book I’ve referred to in the past and have returned to is Olver’s book on Lie groups. It’s very conversational and focuses on many examples and calculations. Reading it again recently has helped connect a couple of ideas that … Continue reading
Lie groups and Lie Algebras – 1
Sources: Maggiore: “A Modern Introduction to Quantum Field Theory” Robert Gilmore: “Lie Groups, Physics, and Geometry” Ballentine: “Quantum Mechanics: A Modern Development” These posts are going to have a lot of questions in them because I have a lot of … Continue reading
Pullback bundle as pullback example (category theory)
Sometimes I think I’m in an odd variation of the game Twister except instead of colored circles, the circles are labeled with topics. Currently I have at least one limb on TQFTs, another limb on Lie theory/representation theory, another limb … Continue reading
Decomposition of Cobordisms (intuitive)
As mentioned previously, Kock has a helical pedagogy in his book. This next post considers the decomposition of cobordisms. What follows isn’t rigorous, I think that’s coming up and will be much more detailed. Here’s the idea, suppose we have … Continue reading