Talks

Hank Chen, Perimeter Institute and University of Waterloo

Drinfel’d double symmetry of the 4d Kitaev model

We construct the 2-Drinfel'd double associated to a finite 2-group G, and compute its braided 2-category of 2-representations, in order to characterize the topological excitations in the 4d toric code and its spin-Z_2 variant. This work relates the categorical and field theoretical approaches toward characterizing higher-dimensional topological phases in existing literature. In particular, we show that particular twists of the underlying 2-Drinfel'd double is responsible for much of the higher-structural properties that arise in gapped topological phases in 4d. We emphasize that this work also displays the first ever instance of higher Tannakian duality for 2-categories.

Jacob Barnett, Perimeter Institute

Locality and Exceptional Points in Pseudo-Hermitian Physics

This talk discusses the role of non-Hermitian operators in fundamental and effective theories of physics. An implicit assumption of the tensor product model of locality is that the inner product factorizes with the tensor product. Quasi-Hermitian quantum frameworks can be used to lift this assumption while preserving the reality of spectra and unitarity. After characterizing local observable algebras and expectation values, I will examine Bell's inequality and its generalizations, the nonlocal games, in the setting of quasi-Hermitian theories. Pseudo-Hermitian operators characterize systems with time-reversal symmetry. These operators exhibit rich perturbative and symmetry-breaking properties that are unparalleled in the Hermitian regime. I will convey some geometric and topological aspects of these features, with emphasis placed on non-interacting many-body systems.
 

"Imsets, introduced by Studený (see Studený, 2005 for details), are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice when applied to directed acyclic graph (DAG) models. In particular, the standard imset for a DAG is in one-to-one correspondence with the independence model it induces, and hence is a label for its Markov equivalence class. We present a proposed extension to standard imsets for maximal ancestral graph (MAG) models, which have directed and bidirected edges, using the parameterizing set representation of Hu and Evans (2020). By construction, our imset also represents the Markov equivalence class of the MAG. We show that for many such graphs our proposed imset defines the model, though there is a subclass of graphs for which the representation does not. We prove that it does work for MAGs that include models with no adjacent bidirected edges, as well as for a large class of purely bidirected models. If there is time, we will also discuss applications of imsets to structure learning in MAGs. This is joint work with Zhongyi Hu (Oxford). References Z. Hu and R.J. Evans, Faster algorithms for Markov equivalence, In Proceedings for the 36th Conference on Uncertainty in Artificial Intelligence (UAI-2020), 2020. M. Studený, Probabilistic Conditional Independence Structures, Springer-Verlag, 2005."

The fundamental nature of dark matter (DM) so far eludes direct detection experiments, but it has left its imprint in the large-scale structure (LSS) of the Universe. I will present a search using cosmic microwave background (CMB) and galaxy surveys for ultra-light DM particle candidates called axions that are well motivated from high energy theory. In combining these datasets, I will discuss how the presence of axions can improve consistency between these probes and, in particular, help alleviate the S_8 cosmological parameter tension (the discrepancy in the amplitude of density fluctuations as inferred from CMB and galaxy data). I will then present complementary searches for ultra-light and light (sub-GeV) DM using a LSS probe called the Lyman-alpha forest. By combining complementary large- and small-scale structure probes, I will demonstrate how current and forthcoming cosmological data will systematically test the nature of DM. In order to model novel DM physics accurately and efficiently in CMB and LSS probes, I will present new machine learning approaches using neural network "emulators" to accelerate DM parameter inference from days to seconds and active learning to reduce massively the computational expense.

Zoom Link: TBD