Borcherds algebras and 2d string theory
Sarah Harrison Stanford University
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Moving Closer to a Detection of nHz-frequency Gravitational Waves with NANOGrav
Scott Ransom National Radio Astronomy Observatory
Beating the Curse of Dimensionality in High-Dimensional Optimal Stopping
David Goldberg (Cornell ORIE)Nilpotent Slodowy slices and W-algebras
Anne Moreau University of Poitiers
Measurement of quantum fields in curved spacetimes
Chris Fewster University of York
On random circuits and their uses in compilation
Earl Campbell University of Sheffield
Beyond BCS: An Exact Model for Superconductivity and Mottness
Philip Phillips University of Illinois Urbana-Champaign
Special Topics in Astrophysics - Numerical Hydrodynamics - Lecture 12
Daniel Siegel University of Greifswald
PIRSA:20100020Asymptotic symmetries and celestial CFT
Laura Donnay SISSA International School for Advanced Studies
Axion-like Relics: New Constraints from Old Comagnetometer Data
Itay Bloch Tel Aviv University
GW190521 - Discovery of Black Holes that Should Not Exist
Karan Jani Pennsylvania State University
Borcherds algebras and 2d string theory
Sarah Harrison Stanford University
Borcherds Kac-Moody (BKM) algebras are a generalization of familiar Kac-Moody algebras with imaginary simple roots. On the one hand, they were invented by Borcherds in his proof of the monstrous moonshine conjectures and have many interesting connections to new moonshines, number theory and the theory of automorphic forms. On the other hand, there is an old conjecture of Harvey and Moore that BPS states in string theory form an algebra that is in some cases a BKM algebra and which is based on certain signatures of BKMs observed in 4d threshold corrections and black hole physics. I will talk about the construction of new BKMs superalgebras arising from self-dual vertex operator algebras of central charge 12, and comment on their relation to physical string theories in 2 dimensions. Based on work with N. Paquette, D. Persson, and R. Volpato.
Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization
Negin Golrezaei (MIT)Motivated by online decision-making in time-varying combinatorial environments, we study the problem of transforming offline algorithms to their online counterparts. We focus on offline combinatorial problems that are amenable to a constant factor approximation using a greedy algorithm that is robust to local errors. For such problems, we provide a general framework that efficiently transforms offline robust greedy algorithms to online ones using Blackwell approachability. We show that the resulting online algorithms have O(T^{1/2}) (approximate) regret under the full information setting. We further introduce a bandit extension of Blackwell approachability that we call Bandit Blackwell approachability. We leverage this notion to transform greedy robust offline algorithms into an O(T^{2/3})(approximate) regret in the bandit setting. Demonstrating the flexibility of our framework, we apply our offline-to-online transformation to several problems at the intersection of revenue management, market design, and online optimization, including product ranking optimization in online platforms, reserve price optimization in auctions, and submodular maximization. We show that our transformation, when applied to these applications, leads to new regret bounds or improves the current known bounds.Moving Closer to a Detection of nHz-frequency Gravitational Waves with NANOGrav
Scott Ransom National Radio Astronomy Observatory
Millisecond Pulsars (MSPs) have become reliable and
extremely stable workhorses of modern astronomy and physics. The
North American Nanohertz Observatory for Gravitational Waves, or
NANOGrav, has been observing growing numbers of these systems for over
15 years, and the data look great. High precision timing of almost 80
MSPs has provided unprecedented sensitivity to the gravitational wave
Universe at nHz-frequencies, where our upper limits are already
constraining the population of super-massive black hole binaries. But
our sensitivity is increasing each year as we continue to add MSPs to
our timing array and develop new techniques to remove systematics due
to the interstellar medium and the uncertain solar system ephemerides.
Meanwhile, though, our observations provide a wide variety of
astrophysics, such as new neutron star mass measurements and
constraints of the dense matter equation of state.Beating the Curse of Dimensionality in High-Dimensional Optimal Stopping
David Goldberg (Cornell ORIE)The sample and computational complexity of reinforcement learning algorithms under the generative model has been a central focus of the literature. Most existing approaches which can guarantee epsilon-optimality require a complexity either dependent on the size of the state space, or which scales exponentially in the time horizon T, in both cases suffering from the curse of dimensionality. Other approaches may be more efficient, but typically either make strong structural assumptions, or do not come with optimality guarantees. We reconcile this dilemma for the celebrated problem of high-dimensional optimal stopping, a special case of RL with important applications to financial engineering, operations research, economics and computer science, and well-known to be computationally challenging when the state space and time horizon are large. We propose the first algorithm with sample and computational complexity polynomial in T, and effectively independent of the underlying state space, which outputs epsilon-optimal stopping policies and value function approximations. Our algorithm is inspired by a novel connection between network flow theory in combinatorial optimization and the classical martingale duality theory for stopping problems, and can be viewed as a higher-order generalization of the celebrated prophet inequalities. Our approach yields an expansion for the value functions as an infinite sum, which is fundamentally different from standard expansions based on backwards induction, with the following properties : 1. each term is the expectation of an elegant recursively defined infimum; 2. the first k terms only require T^k samples to approximate; and 3. truncating at the first k terms yields a (normalized) error of 1/k. The terms of the associated sum can also be viewed as a provably good set of basis functions, which can be efficiently evaluated by simulation, in contrast with past approximate dynamic programming approaches which take a heuristic approach to deriving basis functions. Our work shows that although the state space is exponentially large, one need only explore it to the extent that one can compute these (few) basis functions, which can be done efficiently. Time permitting, we will also explore applications of our approach to other high-dimensional RL problems (including those arising in dynamic pricing and online combinatorial optimization), and discuss connections to parallel and quantum computing. Joint work with Ph.D. student Yilun Chen.Nilpotent Slodowy slices and W-algebras
Anne Moreau University of Poitiers
To any vertex algebra one can attach in a canonical way a certain Poisson variety, called the associated variety. Nilpotent Slodowy slices appear as associated varieties of admissible (simple) W-algebras. They also appear as Higgs branches of the Argyres-Douglas theories in 4d N=2 SCFT’s. These two facts are linked by the so-called Higgs branch conjecture. In this talk I will explain how to exploit the geometry of nilpotent Slodowy slices to study some properties of W-algebras whose motivation stems from physics. This is a joint work with Tomoyuki Arakawa and Jethro van Ekeren (still in preparation).
Measurement of quantum fields in curved spacetimes
Chris Fewster University of York
A standard account of the measurement chain in quantum mechanics involves a probe (itself a quantum system) coupled temporarily to the system of interest. Once the coupling is removed, the probe is measured and the results are interpreted as the measurement of a system observable. Measurement schemes of this type have been studied extensively in Quantum Measurement Theory, but they are rarely discussed in the context of quantum fields and still less on curved spacetimes.
In this talk I will describe how measurement schemes may be formulated for quantum fields on curved spacetime within the general setting of algebraic QFT. This allows the discussion of the localisation and properties of the system observable induced by a probe measurement, and the way in which a system state can be updated thereafter. The framework is local and fully covariant, allowing the consistent description of measurements made in spacelike separated regions. Furthermore, specific models can be given in which the framework may be exemplified by concrete calculations.
I will also explain how this framework can shed light on an old problem due to Sorkin concerning "impossible measurements" in which measurement apparently conflicts with causality.
The talk is based on work with Rainer Verch [Leipzig], (Comm. Math. Phys. 378, 851–889(2020), arXiv:1810.06512; see also arXiv:1904.06944 for a summary) and a recent preprint arXiv:2003.04660 with Henning Bostelmann and Maximilian H. Ruep [York].
On random circuits and their uses in compilation
Earl Campbell University of Sheffield
I will review work by myself and others in recent years on the use of randomization in quantum circuit optimization. I will present general results showing that any deterministic compiler for an approximate synthesis problem can be lifted to a better random compiler. I will discuss the subtle issue of what "better" means and how it is sensitive to the metric and computation task at hand. I will then review specific randomized algorithms for quantum simulations, including randomized Trotter (Su & Childs) and my group's work on the qDRIFT and SPARSTO algorithms. The qDRIFT algorithm is of particular interest as it gave the first proof that Hamiltonian simulation is possible with a gate complexity that is independent of the number of terms in the Hamiltonian. Since quantum chemistry Hamiltonians have a very large ( ~N^4) number of terms, randomization is especially useful in that setting. I will conclude by commenting on a recent Caltech paper with interesting results on the derandomization of random algorithms! Some of the relevant preprints include:
https://arxiv.org/abs/1910.06255
Beyond BCS: An Exact Model for Superconductivity and Mottness
Philip Phillips University of Illinois Urbana-Champaign
High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. In 1992 Hatsugai and Khomoto wrote down a momentum-space model for a Mott insulator which is safe to say was largely overlooked, their paper garnering just 21 citations (6 due to our group). I will show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper's instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state.
Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.
Special Topics in Astrophysics - Numerical Hydrodynamics - Lecture 12
Daniel Siegel University of Greifswald
PIRSA:20100020Asymptotic symmetries and celestial CFT
Laura Donnay SISSA International School for Advanced Studies
Universal relationships between asymptotic symmetries, QFT soft theorems, and low energy observables have reinvigorated attempts at flat space holography. In this talk, I will review recent advances in the celestial holography proposal, where the 4d S-matrix is reconsidered as a 2d correlator on the celestial sphere at null infinity. In this framework, asymptotic particle states are characterized by the point at which they enter or exit the celestial sphere as well as their SL(2,C) Lorentz quantum numbers: namely their conformal scaling dimension and spin instead of the energy and momentum. I will present a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension.
Axion-like Relics: New Constraints from Old Comagnetometer Data
Itay Bloch Tel Aviv University
Abstract: TBD
GW190521 - Discovery of Black Holes that Should Not Exist
Karan Jani Pennsylvania State University
The new gravitational-wave signal GW190521in LIGO and Virgo marks the first observational detection of the elusive intermediate-mass black holes. The detection also confirms there exist a new class of black holes in the mass gap predicted by the pair-instability supernovae theory. In this talk, I will discuss the process that went behind inferring the astrophysical properties of this historic discovery. I would briefly address the alternative scenarios we looked into for a possible exotic origin of this signal, including any violation of General Relativity. For the upcoming ESA/NASA space mission LISA, I would highlight how this discovery opens a unique epoch of multi-band, multi-messenger astronomy.