Scientific Series

I will present a brief introduction to Nested Sampling, a complementary framework to Markov Chain Monte Carlo approaches that is designed to estimate marginal likelihoods (i.e. Bayesian evidences) and posterior distributions. This will include some discussion on the philosophical distinctions and motivations of Nested Sampling, a few ways of understanding why/how it works, some of its pros and cons, and more recent extensions such as Dynamic Nested Sampling. If time/interest permits, I can either (a) highlight how this can work in practice using the public Python package dynesty​ or (b) discuss the more general problem of model selection and why Bayesian evidences may (or may not) be helpful.

Zoom Link: https://pitp.zoom.us/j/95990705337?pwd=VzB4cjhzSDhoM0RCYTNwZHUzUVlzdz09

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

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

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

The volume of the interior of a two-sided eternal black hole classically grows forever. I will derive a microscopic formula for this volume in JT gravity by summing the non-perturbative contribution of higher topologies. The non-perturbative corrections lead to the saturation of the volume of the interior at times exponential in the entropy of the black hole. I will connect the microscopic formula for the volume with properties of a "thermo-averaged" density matrix, in particular with its second Renyi entropy, which I argue to measure the number of nearly orthogonal states visited by time evolution. I will discuss various problems with this interpretation.

Zoom Link: https://pitp.zoom.us/j/99880539557?pwd=VWZiMFI5Rk5pdnNZRE5kalRvUk1Zdz09

Direct detection searches for dark matter are typically optimized to search for weakly interacting particles with masses on the ~GeV scale. But these experiments are, in principle, sensitive to masses as large as approximately the Planck mass, for cross sections much larger than typical Weak-scale cross sections. However, certain assumptions typically made in direct detection analyses break down at such large cross sections, and must be reexamined. In my talk, I will discuss the theoretical considerations that become important for heavy, strongly interacting dark matter, as well as new types of dark matter search that become possible at such high masses and cross sections.

Zoom Link: https://pitp.zoom.us/j/98807962972?pwd=UXFWLzA0N2dPQ3JrVUo4TStmSGtWUT09

Many key cosmological observables have a built-in symmetry under rescaling of all important length scales in the problem. This scaling symmetry can be used to make partial progress toward a complete resolution of the Hubble tension. To exploit the symmetry while respecting observational constraints, we are naturally led to a “mirror world” dark sector. A successful implementation of this scaling symmetry requires a means of increasing the cosmic photon scattering rate that respects observational bounds on the primordial helium abundance. We discuss different ideas that could in principle achieve this rescaling, and discuss their advantages and drawbacks. We finally present some general observations about the fundamental nature of the “Hubble tension".

Zoom Link: https://pitp.zoom.us/j/99678466262?pwd=VTY4cWNFUERhU08vYi9lT09MZjJkdz09

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

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

JT gravity in AdS was shown by Saad, Shenker and Stanford to be described by a matrix ensemble of random hamiltonians. We couple JT to a bulk scalar field and extend the matrix ensemble to include a second matrix, dual to the scalar field. We therefore consider a 2-matrix model that can be thought of as a (better defined) generalization of Eigenstate Thermalization Hypotheses: it is a coupled matrix model of a random hamiltonian and a random operator. The 2-matrix model has an interesting integrability structure: correlation functions are expressed via SL(2,R) 6j-symbols that obey unlacing rules and Yang-Baxter equations. We compute the two-sided 2-point function on the double-trumpet geometry from the matrix model and find agreement with the matter loop contribution in the bulk. Based on work in progress with Jafferis, Kolchmeyer and Sonner.

Zoom Link: https://pitp.zoom.us/j/92268935307?pwd=dytCdTJlWVc3QXkweWxzcy83Sk9PZz09