Talks

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.

The Lagrangian Floer homology of a pair of holomorphic Lagrangian submanifolds of a hyperkahler manifold is expected to simplify, by work of Solomon-Verbitsky and others. This occurs in part because, in this setting, the symplectic action functional, the gradient flow of which computes Lagrangian Floer homology, is the real part of a holomorphic function. As noted by Haydys, thinking of this holomorphic function as a superpotential on an infinite-dimensional symplectic manifold gives rise to a quaternionic analog of Floer's equation for holomorphic strips: the Fueter equation. I will explain how this line of thought gives rise to a `complexification' of Floer's theorem identifying Fueter maps in cotangent bundles to Kahler manifolds with holomorphic planes in the base. This complexification has a conjectural categorical interpretation, giving a model for Fukaya-Seidel categories of Lefshetz fibrations, which should have algebraic implications for the study of Fukaya categories. This is a report on upcoming joint work with Aleksander Doan.

I will discuss a method to associate new types of quantum groups to certain holomorphic Lagrangian fibrations. This algebraic structure controls the enumerative geometry of the variety admitting the Lagrangian fibration in a way analogous to how a quantum group controls the enumerative geometry of a symplectic singularity. Various questions, including the monodromy of the quantum differential equation, can be answered using local-to-global techniques.

Zoom Link: https://pitp.zoom.us/j/99571261442?pwd=NDZTL1dIbXJPNHZwWVcvSEM4M2crZz09

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

What is the nature of neutron stars? Where are r-process elements formed in the Universe? Multi-messenger observations of neutron star mergers might provide us with the key to address these and other important open questions in astrophysics. However, multi-messenger astronomy also poses new challenges to theorists and observers attempting to turn complex data into answers. In this talk, I will review our current theoretical understanding of neutron star mergers, I will discuss how their dynamic is imprinted in their multi-messenger emissions, and I will present recent simulation results and their implications. Finally, I will discuss future challenges and prospective for this field.

Zoom Link: https://pitp.zoom.us/j/93367275850?pwd=YngycnN4ZXFDQUhQb2lVaHY3V2k0UT09

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.

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. I'll explain two approaches to understanding the behavior and the operational significance of quantum complexity in many-body systems. First, I'll consider a simple model on n qubits: We create a random quantum circuit by randomly sampling the gates that compose it. In this model, quantum complexity can be shown to grow linearly in the number of gates until saturating at a value that is exponential in n. This result proves a version of a conjecture by Brown and Susskind in the context of quantum gravity, thereby reinforcing our understanding of the evolution of wormholes in holography. Second, I'll discuss how quantum complexity manifests itself in the operational processes that we can carry out on an n-qubit system. For instance, what resources are necessary to reset an n-qubit memory register to the pure all-zero computational basis state? This approach reveals a connection between thermodynamics and complexity, as we exhibit a trade-off between the thermodynamic work cost that is necessary for the reset procedure and the complexity cost of the procedure. The general trade-off is quantified by a new measure of entropy which directly connects complexity with entropy. I'll discuss the implications of our results and new prospects for many-body physics in the regime where quantum states are of ever increasing complexity.

Joint work with: Jonas Haferkamp, Teja Naga Bhavia Kothakonda, Anthony Munson, Jens Eisert, Nicole Yunger Halpern

 

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