Talks

Many strongly-correlated systems like high Tc cuprates and heavy fermions have interesting features going beyond quasi-particle description. While Sachdev-Ye-Kitaev(SYK) models are exactly solvable models that can provide a platform to study these physics. In this talk, I will discuss interesting features about the SYK models, including extensive zero temperature entropy and maximally chaos. I will also show some generalization of the SYK models and discuss physical insights from them.

The observables of the large-scale structure such as galaxy number density generally depends on the density environment (of a few hundred Mpc). The dependence can traditionally be studied by performing gigantic cosmological N-body simulations and measuring the observables in different density environments. Alternatively, we perform the so-called "separate universe simulations", in which the effect of the environment is absorbed into the change of the cosmological parameters. For example, an overdense region is equivalent to a universe with positive curvature, hence the structure formation changes accordingly compared to the region without overdensity. In this talk, I will introduce the "separate universe mapping", and present how the power spectrum
and halo mass function change in different density environments, which are equivalent to the squeezed bispectrum and the halo bias, respectively. I will then discuss the extension of this approach to inclusion of additional fluids such as massive neutrinos. This allows us to probe the novel scale-dependence of halo bias and squeezed bispectrum caused by different evolutions of the background overdensities of cold dark matter and the additional fluid. Finally, I will present one application of the separate universe simulations to predict the squeezed bispectrum formed by small-scale Lyman-alpha forest power spectrum and large-scale lensing convergence, and compare with the measurement from BOSS Lyman-alpha forest and Planck lensing map.

Finite-size spectra and entanglement both characterize nonlocal physics of quantum systems, and are universal properties of a CFT. I discuss the energy spectrum of the Wilson-Fisher CFT on the torus in the \epsilon and 1/N expansions. I also consider a class of deconfined quantum critical points where the torus spectrum contains signatures of proximate Z2 topological order. Finally, I compute the entanglement entropy of the Wilson-Fisher and Gross-Neveu CFTs in the large N limit, where an exact mapping to free field entanglement is obtained. Comparison is made with numerics.

We explain how a doubled version of the Beilinson-Bernstein localization functor can be understood using the geometry of the wonderful compactification of a group. Specifically, bimodules for the Lie algebra give rise to monodromic D-modules on the horocycle space, and to filtered D-modules on the group that respect a certain matrix coefficients filtration. These two categories of D-modules are related via an associated graded construction in a way compatible with localization, Verdier specialization, and additional structures. This is joint work with David Ben-Zvi and David Nadler.