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2. Introducing Di↵erential Geometry Gravity is geometry. To fully ...
www.damtp.cam.ac.uk/user/tong/gr/two.pdf12 Jun 2021: S T)µ1.µp1.r1.q1.s. = Sµ1.µp1.qT1.r. 1.s (2.24). Given an (r, s) tensor T , we can also construct a tensor of lower rank (r -
3 The Strong Force In the middle of the ...
www.damtp.cam.ac.uk/user/tong/pp/pp3.pdf23 Apr 2021: 3 The Strong Force. In the middle of the 20th century, the number of seemingly “fundamental” particles. exploded. The electron, proton and neutron had long been known. These were joined,. in 1947, by a new particle called the pion, whose role -
3. Introducing Riemannian Geometry We have yet to meet ...
www.damtp.cam.ac.uk/user/tong/gr/three.pdf25 Feb 2021: Claim:. d? F =? J , rµF µ = J (3.24). -
4. The Einstein Equations It is now time to ...
www.damtp.cam.ac.uk/user/tong/gr/four.pdf25 Feb 2021: ṙ2 Ve(r) = E2 (4.24). but this time with the eective potential. ... This tells us that the particle follows a null geodesic. The equation (4.24) gets replaced. -
5. When Gravity is Weak The elegance of the ...
www.damtp.cam.ac.uk/user/tong/gr/five.pdf25 Feb 2021: 1 1. 2He. i!t. (5.24). where, as we mentioned previously, we should take the real part of the right-hand-side. ... S1(0)2 S2(0)2 = R2. The solutions (5.24) tell us how these geodesics evolve. -
6. Black Holes Black holes are among the most ...
www.damtp.cam.ac.uk/user/tong/gr/six.pdf14 Jun 2021: 6. Black Holes. Black holes are among the most enigmatic objects in the universe. They are described. by deceptively simple solutions to the Einstein equations, yet hold a host of insights. and surprises, from the meaning of causal structure, to -
Artificial polariton molecules
www.damtp.cam.ac.uk/user/ngb23/publications/PhysRevB.103.L060507.pdf27 Feb 2021: 1 Moscow, 121205, Russia. (Received 11 June 2020; revised 5 November 2020; accepted 8 February 2021; published 24 February 2021). ... The coupling of two polaritonic/photonic (nonequilib-rium) CCs was studied in the framework of the weak lasingregime -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/popup_final_mjc22 Jul 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM. -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/SIAM_2021_mjc23 Jul 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM. -
Can stable and accurate neural networks always be computed?
www.damtp.cam.ac.uk/user/mjc249/talks/CRUNCH_mjc11 Jun 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM.
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