Talks

In this talk, we will analyze the properties of the bosonic $\nu = 1$ Moore-Read state when used to build a state
which is strongly believed to be a non-Abelian spin-1 chiral spin liquid state [1]. In this state the bosonic $\nu = 1$
Moore-Read Pfaffian wavefunction is interpreted as a wavefunction for a gas of bosons on a 2D square lattice with one flux quantum per plaquette. We investigate the properties of this wavefunction for the case of planar geometry and for the case of the system living on a torus. For the latter case, there are three distinct states corresponding to the three-fold degeneracy of the $\nu = 1$
bosonic Moore-Read state [2]. Our results show that correlation functions in these states become identical in the limit of large system size. Further issues investigated include the result that the three wavefunctions on the torus are linearly independent and orthogonal in the thermodynamic limit. Additionally, the Renyi entanglement entropy is also calculated for different system partitions in order to extract the topological entanglement entropy $\gamma$.

[1] M. Greiter and R. Thomale, Phys. Rev. Lett. 102, 207203 (2009).
[2] S. B. Chung and M. Stone, J. Phys. A: Math. Theor. 40, 4923 (2007).

A pedagogic introduction will be given to: i) Emergent Majorana fermions and Majorana zero modes in certain condensed matter models and ii) Kondo insulators. This will be followed by discussion of a remarkable Quantum Oscillation Anomaly seen in recent experiments in SmB6, a Kondo insulator, by the Cambridge group [1], as providing evidence [2] for presence of Majorana fermi sea, in an unexpected place. We show a counter intuitive result that these Majorana fermions though neutral, exhibit Landau diamagnetism.

[1] B.S. Tan et al., Science, vol.349, pp. 287-29 (2015), arXiv:1507.01129 [1] G. Baskaran, arXiv:1507.03477

Current and near-future cosmological surveys can provide powerful tests of gravity on the largest scales. However, in order to extract this information, it is essential to understand the host of parameter degeneracies which may arise. I present two approaches towards this goal, with a focus on the use of weak gravitational lensing measurements in combination with other probes. First, I discuss a novel expression for a weak lensing power spectrum under alternative theories of gravity. Obtained by considering small deviations from GR, this expression separates various physical effects of modifications to GR, thus allowing a quantitative understanding of degeneracies between gravitational parameters. Second, I present an investigation into the theoretical uncertainty inherent to the popular gravity-testing statistic E_G. By improving our understanding of the theoretical value of E_G, we can use it to make more robust statements about the viability of alternative theories of gravity on cosmological scales.