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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.

Every Cayley graph of a finitely generated group has some basic properties: they are locally finite, connected, and vertex-transitive. These are not sufficient conditions, there are some well known examples of graphs that have all these properties but are non-Cayley. These examples do however "look like" Cayley graphs, which leads to the natural question of if there exist any vertex-transitive graphs that are completely unlike any Cayley graph. I plan to give some of the history of this question, as well as the construction of the example that finally answered it.

Leighton's Theorem states that if two finite graphs have a common universal cover then they have a common finite cover. I will present a new proof of this using groupoids, and then talk about two generalisations of the theorem that can also be tackled with this groupoid approach: one gives us control over the local structure of the common finite cover, and the other deals with graphs of spaces.

I will present a survey of commonly considered notions of negative curvature for groups, focused on generalising properties of Gromov hyperbolic groups.

Property (FA) is one of the `rigidity properties’ defined for groups, concerning the way a group can act on trees. We’ll take a look at why you might be interested in an action on a tree, what the property is, and then investigate which automorphism groups of free products have it.

The last decade or so has seen substantial progress in the theory of (outer) automorphism groups of right-angled Artin groups (RAAGs), spearheaded by work of Charney and Vogtmann. Many of the techniques used for RAAGs also apply to a wider class of groups, graph products of finitely generated abelian groups, which includes right-angled Coxeter groups (RACGs). In this talk, I will give an introduction to automorphism groups of such graph products, and describe recent developments surrounding the outer automorphism groups of RACGs, explaining the links to what we know in the RAAG case.