Talks by two Princeton professors who visited Oxford last week. Dan Marlow gave a talk about luminosity measurements at the Large Hadron Collider, discussing the various technical issues involved when pushing equipment to its limits to test the limits of science. Duncan Haldane spoke about geometry and topological phases of matter, starting from the Gauss-Bonnet theorem and the generalisation by Chern. Interesting history about how Karplus and Luttinger's paper in 1954 (Phys. Rev. 95, 1154–1160) on the anomalous Hall effect was discredited and finally vindicated in 2005.

Fellow graduate student Curt von Keyserlingk gave a talk on the Toric Code too, a toy model involving plaquette and vertex terms in the hamiltonian for the spins. There's a nice pictorial representation of the states of the system, and similar models can lead to what are known as "anyon statistics" for quasiparticles that are neither fermions nor bosons.

Roser Valenti from Goethe University in Frankfurt gave a talk on frustration, using density functional theory to come up with effective models and studying them with quantum Monte Carlo and other methods. Interesting attempt to understand caesium copper chloride and caesium copper bromide by substituting the chlorine atoms with bromine atoms and vice versa.

Martin Rees from Cambridge delivered a public lecture on "The Limits of Science" last week too, and I took the kids to it. He had some encouragement for beginning scientists, who might feel that so many major advances have been made that it's hard to push further forward. His idea was that each advance leads to new questions, and the computational power we have at our disposal is a powerful tool that previous generations did not have. Yet there are likely to be things beyond our ability to comprehend, which require posthuman intelligence. There is a huge gulf between what we can do today and what we should do, whether in research or in public policy, and we need to choose wisely with a longer term view of leaving a fair inheritance for future generations.

The Gauss-Bonnet Theorem is one of the main theorems in Riemannian geometry. Many textbooks lack a complete proof. See John Lee's Riemannian manifolds for an excellent treatment.

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