A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 15:27, 10 April 2020
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<p>[01:00:20] At the mathematical level, an intrinsic theory would be, let's be a little fastidious: the older semi-Riemannian geometry. The study of manifolds with length and angle. But auxiliary geometry is really what's taken off of late since the revolution partially begun at Oxford when Is Singer brought insights from Stony Brook to the U.K. | <p>[01:00:20] At the mathematical level, an intrinsic theory would be, let's be a little fastidious: the older semi-Riemannian geometry. The study of manifolds with length and angle. But auxiliary geometry is really what's taken off of late since the revolution partially begun at Oxford when Is Singer brought insights from Stony Brook to the U.K. | ||
And so we're going to call this fiber bundle theory or modern gauge theory. Geometric Unity is the search for some way to break down the walls between these four boxes. What's natural to one theory is unnatural to another. Semi-Riemannian geometry is dominated by these projection operators as well as the ability | And so we're going to call this fiber bundle theory or modern gauge theory. Geometric Unity is the search for some way to break down the walls between these four boxes. What's natural to one theory is unnatural to another. Semi-Riemannian geometry is dominated by these projection operators as well as the ability to use the Levi-Civita connection. | ||
<p>[01:01:08] Now, some aspects of this are less explored. Torsion tensors are definable in semi-Riemannian geometry, but they are not used to the extent that you might imagine. In the case of fiber bundle theory, the discovery of physicists that the gauge group was fantastically important. [This] came as something of a shock to the mathematicians who had missed that structure, and have since exploited it to great effect. | <p>[01:01:08] Now, some aspects of this are less explored. Torsion tensors are definable in semi-Riemannian geometry, but they are not used to the extent that you might imagine. In the case of fiber bundle theory, the discovery of physicists that the gauge group was fantastically important. [This] came as something of a shock to the mathematicians who had missed that structure, and have since exploited it to great effect. | ||