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Topics will include (but are not limited to): Canonical formulation of constrained systems, The Dirac program, First order formalism of gravity, Loop Quantum Gravity, Spinfoam models, Research at PI and other approaches to quantum gravity.

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.

I’ll review a new, simpler explanation for the large scale geometry of spacetime, presented recently by Latham Boyle and me in arXiv:2201.07279. The basic ingredients are elementary and well-known, namely Einstein’s theory of gravity and Hawking’s method of computing gravitational entropy. The new twist is provided by the boundary conditions we proposed for big bang-type singularities, respecting CPT symmetry and analyticity at the bang with finite Weyl curvature. These boundary conditions allow gravitational instantons for universes with positive Lambda, massless (conformal) radiation and positive or negative space curvature. Using these new instantons, we are able to infer the gravitational entropy for a complete set of quasi-realistic, four-dimensional cosmologies. If the total entropy in radiation exceeds that of Einstein’s static universe, the gravitational entropy exceeds the de Sitter entropy. As the total entropy in radiation is increased further,  the most probable large-scale geometry for the universe becomes increasingly flat, homogeneous and isotropic. I’ll also briefly summarize recent progress towards elaborating this picture into a fully predictive cosmological theory.

Zoom Link: https://pitp.zoom.us/j/95474226765?pwd=clN5UHBnSTFiSVAzM0p3dEdDMzV2Zz09

Among the discoveries in LIGO/Virgo/KAGRA's third observing run are a handful of compact binary coelescences (CBCs) that stand out for one reason or another -- exceptional either because they were the first entry in a previously undetected class of CBCs, or because of the mass, mass ratio, or spins of their component compact objects. After briefly discussing the implications of these observations and their merger rates, I will focus on the tension that has arisen from the discovery of the most massive binaries in LVK's catalog. These binaries have component black holes encroaching on the pair-instability mass gap, where black holes are not expected to be formed directly from stars. I'll discuss an alternate formation channel, where massive black holes are assembled dynamically from repeated binary black hole mergers, and an analysis that constructs a binary black hole population that allows for hierarchical formation in both globular cluster-like and nuclear star cluster-like environments.

Zoom Link: https://pitp.zoom.us/j/94867401133?pwd=bTJmVy8vUk9rb1RvTDlrMzl1ZHdEZz09

This course is designed to introduce modern machine learning techniques for studying classical and quantum many-body problems encountered in condensed matter, quantum information, and related fields of physics. Lectures will focus on introducing machine learning algorithms and discussing how they can be applied to solve problem in statistical physics. Tutorials and homework assignments will concentrate on developing programming skills to study the problems presented in lecture.

Topics will include (but are not limited to): Canonical formulation of constrained systems, The Dirac program, First order formalism of gravity, Loop Quantum Gravity, Spinfoam models, Research at PI and other approaches to quantum gravity.

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.

Quantum error correction and symmetries are two key notions in quantum information and physics. The competition between them has fundamental implications in fault-tolerant quantum computing, many-body physics and quantum gravity. We systematically study the competition between quantum error correction and continuous symmetries associated with a quantum code in a quantitative manner. We derive various forms of trade-off relations between the quantum error correction inaccuracy and three types of symmetry violation measures. We introduce two frameworks for understanding and establishing the trade-offs based on the notions of charge fluctuation and gate implementation error. From the perspective of fault-tolerant quantum computing, we demonstrate fundamental limitations on transversal logical gates. We also analyze the behaviors of two near-optimal codes: a parametrized extension of the thermodynamic code, and quantum Reed–Muller codes.

Zoom Link: TBD

This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced.

Topics will include (but are not limited to): - Quantum error correction in quantum gravity and condensed matter - Quantum information scrambling and black hole information - Physics of random tensor networks and random unitary circuits