Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds

We prove local energy decay estimates for solutions to the inhomogeneous Maxwell system on a generic class of spherically symmetric black holes.Comment: v2. Added some references. Improved exposition and one new diagram. Journal versio

Regularity of Wave-Maps in dimension 2+1

In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps $\Phi:\mathbb{R}^{2+1}\to\mathcal{M}$ into general compact target manifolds $\mathcal{M}$.Comment: 31 page

Computing data for Levin-Wen with defects

We demonstrate how to do many computations for non-chiral topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects. Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate how domain wall fusion and associators can be computed using generalized tube algebra techniques. These domain walls can be both between distinct or identical phases. Additionally, we show how to compute all possible point defects, and the fusion and associator data of these. Worked examples, tabulated data and Mathematica code are provided.Comment: 17+25 pages, many tables and attached cod

Unified Pragmatic Models for Generating and Following Instructions

We show that explicit pragmatic inference aids in correctly generating and following natural language instructions for complex, sequential tasks. Our pragmatics-enabled models reason about why speakers produce certain instructions, and about how listeners will react upon hearing them. Like previous pragmatic models, we use learned base listener and speaker models to build a pragmatic speaker that uses the base listener to simulate the interpretation of candidate descriptions, and a pragmatic listener that reasons counterfactually about alternative descriptions. We extend these models to tasks with sequential structure. Evaluation of language generation and interpretation shows that pragmatic inference improves state-of-the-art listener models (at correctly interpreting human instructions) and speaker models (at producing instructions correctly interpreted by humans) in diverse settings.Comment: NAACL 2018, camera-ready versio

Fusing Binary Interface Defects in Topological Phases: The Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z}) case

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods can be applied to any Levin-Wen model. We also give physical interpretations for each of the defects in the $\mathbb{Z}/p\mathbb{Z}$ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion.Comment: 27+10 pages, 2+5 tables, comments welcom