Talks

In this talk I will provide evidence supporting the Dolan/Nirschl/Osborn conjecture for the precise form of the amplitude of four-point functions of 1/2-BPS operators in N=4 SYM theory at strong coupling and in the large N limit. I will also discuss the methods that allowed the evaluation of amplitudes involving operators of arbitrary conformal dimension.

Quantum theory can be thought of as a noncommutative generalization of Bayesian probability theory, but for the analogy to be convincing, it should be possible to describe inferences among quantum systems in a manner that is independent of the causal relationship between those systems. In particular, it should be possible to unify the treatment of two kinds of inferences: (i) from beliefs about one system to beliefs about another, for instance, in the Einstein-Podolsky-Rosen or "quantum steering" phenomenon, and (ii) from beliefs about a system at one time to beliefs about that same system at another time, for instance, in predictions or retrodictions about a system undergoing dynamical evolution or undergoing a measurement. I will present a formalism that achieves such a unification by making use of "conditional quantum states", a noncommutative generalization of conditional probabilities. I argue for causal neutrality by drawing a comparison with a classical statistical theory with an epistemic restriction. (Joint work with Matthew Leifer).

The talk consists of two parts: (1) Quasi-single inflation, where the isocurvature direction has mass of order Hubble parameter. This part is based on 0911.3380 and new results about higher mass, and a sharp turn in trajectory. (2) Multi-stream inflation, where the inflationary trajectory bifurcates. This part is based on 0903.2123, 1006.5021 and a on-going project on calculating the bifurcation probability in a complicated landscape.

We report on our recent progress to investigate materials classes exhibiting d+id superconductivity, where topologically nontrivial pairing phases can emerge. Specifically, motivated by recent experimental progress, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity. As a function of system parameters such as doping and range of Coulomb interaction, we explain which instability is favored by the system, and analyze the effect of long-range interactions on superconductivity giving rise to a competition between singlet d+id and triplet f wave. We also outline our work in progress for other materials classes which we believe are promising to stabilize such interesting topological superconducting states of matter.

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) will emerge when electrons move in Landau levels. In this talk, I will show FQHE can emergy even in the absence of Landau levels in interacting fermion models and boson models. The non-interacting part of our Hamiltonian contains topologically nontrivial flat band.