A Quantitative Approach to Understanding Online Antisemitism

A new wave of growing antisemitism, driven by fringe Web communities, is an increasingly worrying presence in the socio-political realm. The ubiquitous and global nature of the Web has provided tools used by these groups to spread their ideology to the rest of the Internet. Although the study of antisemitism and hate is not new, the scale and rate of change of online data has impacted the efficacy of traditional approaches to measure and understand these troubling trends. In this paper, we present a large-scale, quantitative study of online antisemitism. We collect hundreds of million posts and images from alt-right Web communities like 4chan's Politically Incorrect board (/pol/) and Gab. Using scientifically grounded methods, we quantify the escalation and spread of antisemitic memes and rhetoric across the Web. We find the frequency of antisemitic content greatly increases (in some cases more than doubling) after major political events such as the 2016 US Presidential Election and the "Unite the Right" rally in Charlottesville. We extract semantic embeddings from our corpus of posts and demonstrate how automated techniques can discover and categorize the use of antisemitic terminology. We additionally examine the prevalence and spread of the antisemitic "Happy Merchant" meme, and in particular how these fringe communities influence its propagation to more mainstream communities like Twitter and Reddit. Taken together, our results provide a data-driven, quantitative framework for understanding online antisemitism. Our methods serve as a framework to augment current qualitative efforts by anti-hate groups, providing new insights into the growth and spread of hate online.Comment: To appear at the 14th International AAAI Conference on Web and Social Media (ICWSM 2020). Please cite accordingl

Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice

In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be "fragile" with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the "obstructed atomic limit" of B. Bradlyn et al., Nature 547, 298--305 (2017). We conclude with some perspectives on topological matter beyond the K-theory classification.Comment: 13 pages, 10 figures v2. accepted versio

Effective action approach to the filling anomaly in crystalline topological matter

In two dimensions, magnetic higher-order topological insulators (HOTIs) are characterized by excess boundary charge and a compensating bulk ``filling anomaly.'' At the same time, without additional noncrystalline symmetries, the boundaries of two-dimensional HOTIs are gapped and featureless at low energies, while the bulk of the system is predicted to have a topological response to the insertion of lattice (particularly disclination) defects. Until recently, a precise connection between these effects has remained elusive. In this work, we point the direction towards a unifying field-theoretic description for the bulk and boundary response of magnetic HOTIs. By focusing on the low-energy description of the gapped boundary of a two-dimensional magnetic HOTI with no time-reversing symmetries, we show that the boundary charge and filling anomaly arise from the gravitational ``Gromov-Jensen-Abanov'' (GJA) response action first introduced in [Phys. Rev. Lett. 116, 126802 (2016)] in the context of the quantum Hall effect. As in quantum Hall systems the GJA action cancels apparent anomalies associated with bulk response to disclinations, allowing us to derive a concrete connection between the bulk and boundary theories of HOTIs. We show how our results elucidate the connection between higher order topology and geometric response both in band insulators, and point towards a new route to understanding interacting higher order topological phases beyond the simple cases considered here.Comment: v2: accepted version v1: 14+epsilon page