Nonabelianization of Higgs bundles

The character varieties of representations of a surface group into the Lie groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of the moduli space of Higgs bundles. We show that the fibres of the integrable system in these cases are not abelian varieties, but are instead moduli spaces of rank 2 bundles on a spectral curve, satisfying natural stability conditions

A trust model for spreading gossip in social networks

We introduce here a multi-type bootstrap percolation model, which we call T-Bootstrap Percolation (T-BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose vertices have different labels corresponding to the type of role the person plays in the network (e.g. a student, an educator, etc.). Once an initial set of vertices of G is randomly selected to be carrying a gossip (e.g. to be infected), the gossip propagates to a new vertex provided it is transmitted by a minimum threshold of vertices with different labels. By considering random graphs, which have been shown to closely represent social networks, we study different properties of the T-BP model through numerical simulations, and describe its implications when applied to rumour spread, fake news, and marketing strategies.Comment: 9 pages, 9 figure

The Phone Walkers: A study of human dependence on inactive mobile devices

The development of mobile phones has largely increased human interactions. Whilst the use of these devices for communication has received significant attention, there has been little analysis of more passive interactions. Through census data on casual social groups, this work suggests a clear pattern of mobile phones being carried in people's hands, without the person using it (that is, not looking at it). Moreover, this study suggests that when individuals join members of the opposite sex there is a clear tendency to stop holding mobile phones whilst walking. Although it is not clear why people hold their phones whilst walking in such large proportions (38% of solitary women, and 31% of solitary men), we highlight several possible explanation for holding the device, including the need to advertise status and affluence, to maintain immediate connection with friends and family, and to mitigate feelings related to anxiety and security.Comment: To appear in "Behaviour". 21 pages; 7 figures; Appendix in journal version onl

Cayley and Langlands type correspondences for orthogonal Higgs bundles

Through Cayley and Langlands type correspondences, we give a geometric description of the moduli spaces of real orthogonal and symplectic Higgs bundles of any signature in the regular fibres of the Hitchin fibration. As applications of our methods, we complete the concrete abelianization of real slices corresponding to all quasi-split real forms, and describe how extra components emerge naturally from the spectral data point of view.Comment: 34 pages, comments welcomed

Higgs bundles and exceptional isogenies

We explore relations between Higgs bundles that result from isogenies between low-dimensional Lie groups, with special attention to the spectral data for the Higgs bundles. We focus on isogenies onto $SO(4,C)$ and $SO(6,C)$ and their split real forms. Using fiber products of spectral curves, we obtain directly the desingularizations of the (necessarily singular) spectral curves associated to orthogonal Higgs bundles. In the case of $SO(6,C)$ our construction can be interpreted as a new description of Recillas' trigonal construction.Comment: Inadvertent omission in Acknowledgements correcte