Talks

It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries. The Euclidean case yields a ultraviolet cutoff in the form of a bandlimit, and this then allows one to apply the powerful Shannon sampling theorem of classical information theory which establishes the equivalence between continuous and discrete representations of information. As a consequence, one obtains discrete representations of fields which are more subtle than a simple discretization of space, and are in fact equivalent to a continuum representation. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. We then examine the Lorentzian symmetry generalization. This case leads to a Lorentz-invariant analogue of bandlimitation, and we discuss the nature of the corresponding sampling theory.

In this talk I will present a construction of relative Bridgeland stability conditions that appeared in my work on stability of topological Fukaya categories of surfaces. This construction gives a local-to-global tool for constructing stability conditions. I will explain what technical features of such Fukaya categories render this construction useful in their context, and time allowing discuss the challenges involved in applying these ideas to other contexts such as Bridgeland-Smith type stability conditions and topological Fukaya categories with coefficients.

Simulations that numerically solve Einstein's equations are the only means to accurately predict the outcome of the merger of two black holes. The most important outputs from these simulations are the gravitational waveforms, and the mass and spin of the final black hole formed after the merger. The waveforms are used in extracting astrophysical information from detections, while the final mass and spin are used in testing general relativity. Unfortunately, these simulations are too expensive for direct use in data analysis; each simulation can take a month on a supercomputer. Surrogate modeling is a data-driven approach to modeling, that uses machine learning like techniques to interpolate between hundreds of existing simulations. In this talk, I will discuss some recent developments in surrogate modeling, including a new 7-dimensional model that fully captures the effects of precession; the wobbling of the orbit caused when the black holes’ spin axes aren’t perpendicular to the plane of the orbit. This model reproduces the waveform as well as the final black hole's mass and spin as accurately as the simulations themselves, while taking only a fraction of a second to evaluate on a laptop.

Since the discovery of the first exoplanets in the early 1990s, we have detected more than 4,000 worlds beyond our solar system. Many of these are similar in size to our Earth, leading to an obvious question: could any be habitable?

For now, we typically only know the size and orbit of these planets, but nothing about their surface conditions. Although we cannot know for sure if these worlds could support life, we can use models to speculate on what we might find there.

In her Nov. 6 talk at Perimeter Institute, astrophysicist and author Elizabeth Tasker will take audiences for a speculative stroll through a few of the alien worlds we’ve discovered in the galaxy, and ponder whether someone else may already call them home.

Elizabeth Tasker is an astrophysicist at the Japan Aerospace Exploration Agency (JAXA). Her research explores the formation of stars and planets using computer simulations. She is particularly interested in how diverse planets might be and what different conditions might exist beyond our Solar System. Elizabeth is also a keen science communicator and writer for the NASA NExSS “Many Worlds” online column. Her popular science book, The Planet Factory, was published in Canada last April.

Connections between 2D gapped quantum phases and the anyon fusion theory have been proven in various ways under different settings. In this work, we introduce a new framework connecting them by only assuming a conjectured form of entanglement area law for 2D gapped systems. We show that one can systematically define topological charges and fusion rules from the area law alone, in a well-defined way. We then derive the fusion rules of charges satisfy all the axioms required in the algebraic theory of anyons. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy, this term is shown to be equal to the logarithm of the total quantum dimension of the anyon theory we defined. 

Many complex systems have a generative, or linguistic, aspect: life is written in the language of DNA; protein structure is written in a language of amino acids, and human endeavour is often written in text. Are there universal aspects of the relationship between sequence and structure? I am trying to answer this question using models of random languages. Recently I proposed a model of random context-free languages [1] and showed using simulations that the model has a transition from an unintelligent phase to an ordered phase. In the former, produced sequences look like noise, while in the latter they have a nontrivial Shannon entropy; thus the transition corresponds to the emergence of information-carrying in the language. 

In this talk I will explain the basics of natural language syntax, without assuming any prior knowledge of linguistics. I will present the results from the model above, and explain how the model is related to complex matrix models with disorder [2].

[1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.128301

[2] https://arxiv.org/abs/1902.07516

Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many well-known obstructions to such a description. Here, we trace exactly how such obstructions arise in the regime between nonrelativistic quantum mechanics and relativistic quantum field theory. Perhaps unexpectedly, we find that in the nonrelativistic limit of QFT, there are persisting issues with the localizability of particle states. Related via the Reeh-Schlieder theorem, we also show that the fate of ground state entanglement and the Unruh effect is nontrivial in the nonrelativistic limit.

QFTs in 2+1 dimensions are powerful systems to understand the emergence of mass-gap and particle spectrum in QCD-like theories that describe our 3+1 dimensional world. Recently, these 2+1 dimensional systems have attracted even more attention due to conjectured dualities between seemingly very different theories and due to their applications to condensed matter systems. In this talk, I will describe our numerical investigations of the infrared behaviors of 2+1 dimensional U(1) and SU(N) gauge theories coupled to many favors of massless fermions using lattice regularization. I will also explain how lattice formulation is a potential tool to study and check particle-vortex dualities.