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#gauge_theory #math #physics #MobiusStrip #orientation #determinant #exterior_algebra

To go deeper into gauge theory, we have to talk about differential forms and that requires setting up the exterior algebra. To get there, we discuss minus signs (in topology and linear algebra), orientation, and the determinant. Created by Timothy Nguyen.

Prerequisites: Linear algebra

Note: Apologies for lots of audio problems in this video! I used a different mic configuration and it caused lots of background noise especially 1:09-9:00 and 58:48-1:07:39 if you're listening with headphones. Will learn from this mistake!

Correction:
1:03:05: a11*a22 not a11*a12 in computation of determinant

Timestamps:
00:00 : Intro
01:09 : The Mobius strip
09:55 : Orientation
12:31: Orientation in terms of handedness in low dimensions
20:33 : Determinant
34:34 : Mobius strip in n-dimensions
36:16 : Exterior algebra
41:28 : Example computations with the exterior algebra
48:44 : kth exterior power
51:58 : dimension of kth exterior power
54:28 : The full exterior algebra
58:55 : Determinant reformulated in terms of the exterior algebra
1:08:08 : Easy consequence of reformulation: det(AB) = det(A)det(B). The power of higher level conceptualization.
1:14:04 : Other applications of the exterior algebra

Lecture pdf: https://tinyurl.com/yht4ddfp

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