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Multilayer networks are a way to represent dependent connectivity patterns — e.g., time-dependence, multiple types of interactions, or both — that arise in many applications and which are difficult to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as communities, to discover features that lie between the microscale and the macroscale. We introduce a framework for the construction of generative models for mesoscale structure in multilayer networks.  We model dependency at the level of partitions rather than with respect to edges, and treat the process of generating a multilayer partition separately from the process of generating edges for a given multilayer partition. Our framework can admit many features of empirical multilayer networks and explicitly incorporates a user-specified interlayer dependency structure. We discuss the parameters and some properties of our framework, and illustrate an example of its use with benchmark models for multilayer community-detection tools. 

Using non-minimal pure spinor superspace, Cederwall has constructed BRST-invariant actions for D=10 super-Born-Infeld and D=11 supergravity which are quartic in the superfields. But since the superfields have explicit dependence on the non-minimal pure spinor variables, it is non-trivial to show these actions correctly describe super-Born-Infeld and supergravity. In this talk, I will expand solutions to the equations of motion from the pure spinor action for D=10 abelian super Born-Infeld to leading order around the linearized solutions and show that they correctly describe the interactions expected. If I have time, I will explain how to generalize these ideas to D=11 supergravity.

In 1982, Gromov introduced bounded cohomology to give estimates on the minimal volume of manifolds. Since then, bounded cohomology has become an independent and active research field. In this talk I will give an introduction to bounded cohomology, state many open problems and relate it to other fields. 

I will discuss the basics of normal surface theory, and how they were used to give an algorithm for deciding whether a given diagram represents the unknot. This version is primarily based on Haken's work, with simplifications from Schubert and Jaco-Oertel.
 

Polycyclic groups either have polynomial growth, in which case they are virtually nilpotent, or exponential growth. I will give two interesting examples of "small" polycyclic groups which are extensions of $\mathbb{R}^2$ and the Heisenberg group by the integers, and attempt to justify the claim that they are small by sketching an argument that every exponential growth polycyclic group contains one of these.

You’re an amateur investigator hired to uncover the mysterious goings on of a dark cult. They call themselves Geometric Group Theorists and they’re under suspicion of pushing humanity’s knowledge too far. You’ve tracked them down to their supposed headquarters. Foolishly, you enter. Your mind writhes as you gaze unwittingly upon the Eldritch horror they’ve summoned… Group Theory! You think fast; donning the foggy glasses of quasi-isometry, you prevent your mind shattering from the unfathomable complexity of The Beast. You spy a weak spot and the phrase `Gromov Hyperbolicity’ flashes across your mind. You peer deeper, further, forever… only to find yourself somewhere rather familiar, strange, but familiar… no, self-similar! You’ve fought with fractals before, this weirdness can be tamed! Your insight is sufficient and The Beast retreats for now.
In other words, given an infinite group, we associate to it an infinite graph, called a Cayley graph, which gives us a notion of the ‘geometry’ of a group. Through this we can ask what kind of groups have hyperbolic geometry, or at least an approximation of it called Gromov hyperbolicity. Hyperbolic groups are quite a nice class of groups but a large one, so we introduce the Gromov boundary of a hyperbolic group and explain how it can be used to distinguish groups in this class.

"Fibre theorems" in the style of Quillen's fibre lemma are versatile tools used to study the topology of partially ordered sets. In this talk, I will formulate two of them and explain how these can be used to determine the homotopy type of the complex of (conjugacy classes of) free factors of a free group.
The latter is joint work with Radhika Gupta (see https://arxiv.org/abs/1810.09380).

A core problem in the study of manifolds and their topology is that of telling them apart. That is, when can we say whether or not two manifolds are homeomorphic? In two dimensions, the situation is simple, the Classification Theorem for Surfaces allows us to differentiate between any two closed surfaces. In three dimensions, the problem is a lot harder, as the century long search for a proof of the Poincaré Conjecture demonstrates, and is still an active area of study today.
As an early pioneer in the area of 3-manifolds Seifert carved out his own corner of the landscape instead of attempting to tackle the entire problem. By reducing his scope to the subclass of 3-manifolds which are today known as Seifert fibred spaces, Seifert was able to use our knowledge of 2-manifolds and produce a classification theorem of his own.
In this talk I will define Seifert fibred spaces, explain what makes them so much easier to understand than the rest of the pack, and give some insight on why we still care about them today.