Search Talks

From a probabilistic perspective, 2D quantum gravity is the study of natural probability measures on the space of all possible geometries on a topological surface. One natural approach is to take scaling limits of discrete random surfaces. Another approach, known as Liouville quantum gravity (LQG), is via a direct description of the random metric under its conformal coordinate. In this talk, we review both approaches, featuring a joint work with N. Holden proving that uniformly sampled triangulations converge to the so called pure LQG under a certain discrete conformal embedding.

High resolution hydrodynamic simulations of galaxy formation are powerful tools, which can provide important information on the properties of the dark matter halo. Combined with the information obtained from the second data release of the Gaia satellite, simulations can significantly improve our understanding of the dark matter distribution in the Solar neighborhood. Determining the local dark matter velocity distribution is crucial for the correct analysis and interpretation of data from dark matter direct detection experiments. I will discuss the local dark matter distribution of Milky Way-like galaxies extracted from state-of-the-art hydrodynamic simulations, and present an analysis of direct detection data using this distribution. I will also discuss the properties of the dark matter component of the radially anisotropic stellar population recently discovered in the Gaia data, using the Auriga simulations. In particular, I will present the local dark matter density and velocity distributions of the simulated Milky Way-like galaxies with and without the anisotropic substructure, and discuss their implications for dark matter direct detection.

We discuss a new class of quantum phase transitions --- Deconfined Mott Transition (DMT) --- that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and an insulator without emergent neutral Fermi surface. We construct a unified U(2) gauge theory to describe a variety of metallic and insulating phases, which include Fermi liquids, fractionalized Fermi liquids (FL*), conventional insulators and quantum spin liquids, as well as the quantum phase transitions between them. Using the DMT as a basic building block, we propose a distinct quantum phase transition --- Deconfined Metal-Metal Transition (DM2T) --- that describes a continuous transition between two metallic phases, accompanied by a jump in the size of their Fermi surfaces (also dubbed a 'Fermi transition'). We study these new classes of deconfined metallic quantum critical points using a renormalization group framework at the leading nontrivial order in a controlled double-expansion and comment on the various interesting scenarios that can emerge going beyond this leading order calculation.