In this talk we will discuss a problem that was worked on during MISGSA 2020, a Study Group held in January at The University of Zululand, South Africa.

We look at a communication network with two types of users - Primary users (PU) and Secondary users (SU) - such that we reduce the network to a set of overlapping sub-graphs consisting of SUs indexed by a specific PU. Within any given sub-graph, the PU may be communicating at a certain fixed frequency F. The respective SUs also wish to communicate at the same frequency F, but not at the expense of interfering with the PU signal. Therefore if the PU is active then the SUs will not communicate.

In an attempt to increase information throughput in the network, we instead allow the SUs to communicate at a different frequency G, which may or may not interfere with a different sub-graph PU in the network, leading to a multi-objective optimisation problem.

We will discuss not only the problem formulation and possible approaches for solving it, but also the pitfalls that can be easily fallen into during study groups.

In this talk, we will discuss two-dimensional theories with discrete

one-form symmetries, examples (which we have been studying

since 2005), their properties, and gauging of the one-form symmetry.

Their most important property is that such theories decompose into a

disjoint union of theories, recently deemed `universes.'

This decomposition has the effect of restricting allowed nonperturbative

sectors, in a fashion one might deem a `multiverse interference effect,'

which has had applications in topics including Gromov-Witten theory and

gauged linear sigma model phases.  After reviewing one-form symmetries

and decomposition in general, we will discuss a particular 

example in detail to explicitly illustrate these properties and 

to demonstrate how

gauging the one-form symmetry projects onto summands in the

decomposition.  If time permits, we will briefly review

analogous phenomena in four-dimensional theories with three-form symmetries,

as recently studied by Tanizaki and Unsal.

In this talk, I will argue how the observation that four-dimensional N=2 superconformal field theories are interconnected via the operation of Higgsing can be turned into an effective method to construct such SCFTs. A fundamental role is played by the (generalized) free field realization of the associated VOAs.

Here, a connection is a algebraic structure that is weaker than an algebra and stronger than a module. I will define this structure and give examples. I will then define the quantum product and explain how connections capture important properties of this product. I will finish by stating a new result which describes how this extends to equivariant Floer cohomology. No knowledge of symplectic topology will be assumed in this talk.
 

Hawkes processes are a class of point processes used to model self-excitation and cross-excitation between different types of events. They are characterized by the auto-regressive structure of their conditional intensity, and there exists several extensions to the original linear Hawkes model. In this talk, we start by defining Hawkes processes and give a brief overview of some of their basic properties. We then review some approaches to parametric and non-parametric estimation of Hawkes processes and discuss some applications to problems with large data sets in high frequency finance and social networks.