5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this talk, we extend this connection and provide a geometric realization of brane configurations including 7-branes. Along the way, we also review techniques developed in the past few years to describe the Higgs branch of these 5d SCFTs, including magnetic quivers and Hasse diagram for symplectic singularities. 

Data sets of self-reported online resumes are a valuable tool to understand workers' career trajectories and how workers may adapt to the changing demands of employers. However, the sample of workers that choose to upload their resumes online may not be representative of a nation's workforce. To understand the advantages and limitations of these datasets, we analyze a data set of more than 1 Million online resumes and compare the findings with a administrative data from the Current Population Survey (CPS).
 

We model a tokamak fusion reaction, combining Maxwell's equations with the Navier-Stokes equations, the heat equation and the Seebeck effect giving a model of thermoelectric magnetohydrodynamics (TEMHD). At leading order, we showed that the free surface must be flat, that the pressure is constant, and that the temperature decouples from the governing equations relating the fluid velocity and magnetic field. We also find that the fluid flow is driven entirely by the temperature gradient normal to the free surface. Using singular perturbation methods we obtained velocity profiles which exhibit so-called Hartmann layers and thicker side layers. The role of the aspect ratio has been seldom considered in classical MHD duct flow literature as a varying parameter. Here, we show it's importance and derive a relationship between the aspect ratio and Hartmann number that maximises flow rate of fluid down the duct.

Shortwave radiation penetrating beneath an ice-sheet surface can cause internal melting and the formation of a near-surface porous layer known as the weathering crust, a dynamic hydrological system that provides home to impurities and microbial life. We develop a mathematical model, incorporating thermodynamics and population dynamics, for the evolution of such layers. The model accounts for conservation of mass and energy, for internal and surface-absorbed radiation, and for logistic growth of a microbial species mediated by nutrients that are sourced from the melting ice. I will discuss one-dimensional steadily melting solutions of the model, which suggest a range of changes in behaviour of the weathering crust and its microbial community in response to climate change. In addition, time-dependent solutions of the model give insight into the formation and removal of the weathering crust in frequently changing weather conditions.