C1

When Gromov defined non-positively curved cube complexes no one knew what they would be useful for.
Decades latex they played a key role in the resolution of the Virtual Haken conjecture.
In one of the early forays into experimenting with cube complexes, Aitchison, Matsumoto, and Rubinstein produced some nice results about certain "cubed" manifolds, that in retrospect look very prescient.
I will define non-positively curved cube complexes, what it means for a 3-manifold to be cubed, and discuss what all this Haken business is about.
 

A graph of groups decomposition is a way of splitting a group into smaller and hopefully simpler groups. A natural thing to try and do is to keep splitting until you can't split anymore, and then argue that this decomposition is unique. This is the idea behind JSJ decompositions, although, as we shall see, the strength of the uniqueness statement for such a decomposition varies depending on the class of groups that we restrict our edge groups to

Many complex systems can be represented as networks. However, it is often not possible or even desirable to observe the entire network structure. For example, in social networks, it is often difficult to obtain samples of large networks due to commercial sensitivity or privacy concerns relating to the data. However, it may be possible to provide a coarse grained picture of the graph given knowledge of the distribution of different demographics (e.g age, income, location, etc…) in a population and their propensities for forming ties between each other.

I will explore the degree to which it is possible to influence Ising systems, which are commonly used to model social influence, on unobserved graphs. Using both synthetic networks (stochastic blockmodels) and case studies of real world social networks, I will demonstrate how simple models which rely only on a coarse grained description of the system or knowledge of only the underlying external fields can perform comparably to more expensive optimization algorithms.

Cities and their inter-connected transport networks form part of the fundamental infrastructure developed by human societies. Their organisation reflects a complex interplay between many natural and social factors, including inter alia natural resources, landscape, and climate on the one hand, combined with business, commerce, politics, diplomacy and culture on the other. Nevertheless, despite this complexity, there has been some success in capturing key aspects of city growth and network formation in relatively simple models that include non-linear positive feedback loops. However, these models are typically embedded in an idealised, homogeneous space, leading to regularly-spaced, lattice-like distributions arising from Turing-type pattern formation. Here we argue that the geographical landscape plays a much more dominant, but neglected role in pattern formation. To examine this hypothesis, we evaluate the weighted distance between locations based on a least cost path across the natural terrain, determined from high-resolution digital topographic databases for Italy. These weights are included in a co-evolving, dynamical model of both population aggregation in cities, and movement via an evolving transport network. We compare the results from the stationary state of the system with current population distributions from census data, and show a reasonable fit, both qualitatively and quantitatively, compared with models in homogeneous space. Thus we infer that that addition of weighted topography from the natural landscape to these models is both necessary and almost sufficient to reproduce the majority of the real-world spatial pattern of city sizes and locations in this example.

In many applications we are confronted with the following scenario: we observe snapshots of data describing the state of a system at particular times, and based on these observations we want to infer the (dynamical) interactions between the entities we observe. However, often the number of samples we can obtain from such a process are far too few to identify the network exactly. Can we still reliable infer some aspects of the underlying system?
Motivated by this question we consider the following alternative system identification problem: instead of trying to infer the exact network, we aim to recover a (low-dimensional) statistical model of the network based on the observed signals on the nodes.  More concretely, here we focus on observations that consist of snapshots of a diffusive process that evolves over the unknown network. We model the (unobserved) network as generated from an independent draw from a latent stochastic block model (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We present simple spectral algorithms that provably solve the partition and parameter inference problems with high-accuracy.

In an increasingly urbanized world, where cities are changing continuously, it is essential for policy makers to have access to regularly updated decision-making tools for an effective management of urban areas. An example of these tools is the delineation of cities into functional areas which provides knowledge on high spatial interaction zones and their socioeconomic composition. In this paper, we presented a method for the structural analysis of a city, specifically for the determination of its functional areas, based on communities detection in graphs. The nodes of the graph correspond to geographical units resulting from a cartographic division of the city according to the road network. The edges are weighted using a Gaussian distance-decay function and the amount of spatial interactions between nodes. Our approach optimize the modularity to ensure that the functional areas detected have strong interactions within their borders but lower interactions outside. Moreover, it leverages on POIs' entropy to maintain a good socioeconomic heterogeneity in the detected areas. We conducted experiments using taxi trips and POIs datasets from the city of Porto, as a study case. Trough those experiments, we demonstrate the ability of our method to portray functional areas while including spatial and socioeconomic dynamics.
 

A group splits as an HNN-extension if and only if the rank of its abelianisation is strictly positive. If we fix a class of groups one may ask a few questions about these splittings: How distorted are the vertex and edge groups? What form can the vertex and edge groups take? If they remain in our fixed class, do they also split? If so, under iteration will we terminate at something nice? In this talk we will answer all these questions for the class of one-relator groups and go through an example or two. Time permitting, we will also discuss possible generalisations to groups with staggered presentations.

We will answer the following question: given a finite simplicial complex X acted on by a finite group G, which object stores the minimal amount of information about the symmetries of X in such a way that we can reconstruct both X and the group action? The natural first guess would be the quotient X/G, which remembers one representative from each orbit. However, it does not tell us the size of each orbit or how to glue together simplices to recover X. Our desired object is, in fact, a complex of groups. We will understand two processes: compression and reconstruction and see primarily through an example how to answer our initial question.

The mapping class group of a surface is a group of homeomorphisms of that surface, and these groups have been very well studied in the last 50 years. The talk will be focused on a way to understand such a group by looking at the subsurfaces of the corresponding surface; this is the so-called "Masur-Minsky hierarchy machinery". We'll finish with a non-technical discussion of hierarchically hyperbolic groups, which are a popular area of current research, and of which mapping class groups are important motivating examples. No prior knowledge of the objects involved will be assumed.