Congratulations on great presentations everyone. To comment on particular presentation, I really enjoyed Gregory Johnson’s talk on Geometrical Phases. Most of this stuff was very alien to me, as it is physics and, moreover, explored areas of mathematics I am not familiar with. But, although Gregory’s presentation explored very advanced and interesting topics, it has also inspired me to learn more about physics, and I have ended up learning some interesting information on construction of gauges. Though I still don’t have physical intuition, looking up into things I wrote in my notes, made me learn about mathematical meanings of principle and fiber bundles, construction of gauge connections and their relation to Lie curvature 2-forms, so it really expanded my interests into intersection of physics and topology/differential geometry. Also the fact about entanglement being related to 7th homotopy group of a 4-sphere being Z blew me away.
April 15, 2018
Week 1 of Presentations
1 Comment
gljohns3
April 16, 2018 — 11:22
Awesome. Thanks! The entanglement piece is in some papers titled something like “Hopf fibrations and Qubits.” Qubits can be a few things, but in this context they are taken the be the spin states of electrons. One electron gives S^3 and two electrons gives S^7 (three elctrons gives S^15) and the homotopy maps are another form of the Hopf fibrations. Even more fascinating is that its all related to the way reals go to the complex go to quaternions go to octionions and then they’re no longer “nice.” I’ve written a paper on it actually (wasn’t published though)… Glad my talk had that effect!