Talks

We examine the interplay of symmetry and topological order in 2+1D topological phases of matter. We define the topological symmetry group, characterizing symmetry of the emergent topological quantum numbers, and describe its relation with the microscopic symmetry of the physical system.

We then derive a general classification of symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a general algebraic theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter with symmetry. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic defects are turned into deconfined quasiparticle excitations, which results in a different topological phase.

I will discuss recent work studying universal properties of gravity in anti-de Sitter (AdS) spacetime from the perspective of conformal field theory (CFT). After reviewing relevant aspects of the AdS/CFT correspondence, I will demonstrate that all CFTs in three or more dimensions possess a spectrum of operators consistent with long-distance locality and Newtonian gravity in AdS. In generalizing these results to two-dimensional CFTs, I will then show that operators with large scaling dimension create classical backgrounds in the limit of large central charge. This result can be directly related to eigenstate thermalization in 2d CFTs and black hole geometries in 3d AdS. I will conclude by discussing methods for going beyond this large central charge limit in 2d and for studying black holes in higher dimensions.

Photometric surveys are often larger and extend to fainter magnitudes than spectroscopic samples, and can therefore yield more precise cosmological measurements. However, photometric data are significantly contaminated by multiple sources of systematics, either intrinsic, observational, or instrumental. These systematics affect the properties of the raw images in complex ways, propagate into the final catalogues, and create spurious spatial correlations. Some of these correlations may also be imprinted in spectroscopic catalogues, since the latter rely on targets selected from imaging data. Therefore, not just precise — but also accurate — cosmological inferences from imaging surveys require careful mitigation of spatially-varying systematics. I will present a new framework of extended mode projection to robustly mitigate the impact of such systematics on power spectrum measurements. I will demonstrate the effectiveness of the technique, showing constraints on primordial non-Gaussianity using the clustering of 800,000 photometric quasars from the Sloan Digital Sky Survey in the redshift range 0.5 < z < 3.5. Finally, I will present a framework to map the observing conditions of the Science Verification data in the Dark Energy Survey (DES) and incorporate them into end-to-end simulations of the DES transfer function. The considerations presented here are relevant to all multi-epoch surveys, and will be essential for exploiting future high-cadence surveys such as the Large Synoptic Survey Telescope (LSST), which will require detailed null-tests and realistic end-to-end image simulations for correct cosmological inferences.