A groupoid approach to noncommutative T-duality

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following two directions. First, bundles of groups other than tori, even bundles of some nonabelian groups, can be dualized. Second, bundles whose duals are families of noncommutative groups (in the sense of noncommutative geometry) can be treated, though in this case the base space of the bundles is best viewed as a topological stack. Some methods developed for the construction may be of independent interest. These are a Pontryagin type duality that interchanges commutative principal bundles with gerbes, a nonabelian Takai type duality for groupoids, and the computation of certain equivariant Brauer groups.Comment: Same theorems, typos correcte

Historical Amnesia: British and U.S. Intelligence, Past and Present

Many intelligence scandals in the news today seem unprecedented - from Russian meddling in the 2016 U.S. Presidential election, to British and U.S. intelligence agencies monitoring activities of their citizens. They seem new largely because, traditionally, intelligence agencies on both sides of the Atlantic were excessively secretive about their past activities: even the names “GCHQ” and “NSA” were airbrushed from declassified records, and thus missing from major historical works and scholarship on on post-war international relations. The resulting secrecy about British and U.S. intelligence has led to misunderstandings and conspiracy theories in societies about them. Newly opened secret records now reveal the long history of many subjects seen in today’s news-cycle: Anglo-American intelligence cooperation, interference by countries in foreign elections, disinformation, and the use and abuse of intelligence by governments. Newly declassified records also add to our understanding of major chapters of international history, like Britain’s post-war end of empire. Without overcoming our historical amnesia disorder about U.S. and British intelligence, citizens, scholars and policy-makers cannot hope to understand the proper context for what secret agencies are doing today

On the Uncertainty of Archive Hydrographic Datasets

As the international hydrographic community continues to address the question of the irreducible uncertainty in modern surveys, we must ask how we do the same with archived Vertical Beam Echosounder (VBES) and leadline datasets. The ONR funded Strataform project surveyed an area of the New Jersey shelf around 39◦12’N 72◦50’W using an EM1000 Multibeam Echosounder (MBES). This area is also covered by NOAA surveys from 1936- 38 (assumed to be leadline) and 1975-76 (VBES). By comparison of the archival soundings to the MBES data, estimates of measurement error for the archival surveys are constructed as a function of depth. The analysis shows that archival leadline smoothsheets are heavily biased in deeper water because of ‘hydrographic rounding’ and may be unrecoverable, but that the VBES data appear approximately unbiased and may be used to construct products compatible with modern surveys. Estimates of uncertainty for a surface model generated from the archive data are then constructed, taking into account measurement, interpolation, and hydrographic uncertainty (addressing the problems of unobserved areas and surface reconstruction stability). Finally, the paper addresses the generality of the method, and its implications for the community’s duty to convey our uncertainty to the end user

Processing mathematics through digital technologies: A reorganisation of student thinking?

This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking

Visual perturbances in digital pedagogical media

Several studies have investigated how the formation of informal conjectures, and the dialogue they evoke, might influence young children’s learning trajectories, and enhance their mathematical thinking. In a digital environment, the visual output and its distinctive qualities can lead to interpretation and response of a particular nature. In this paper the notion of visual perturbance is explored, and situated within the data obtained, when ten-year-old children engaged in number investigations in a spreadsheet environment