# Superconductors in hyperbolic space

Superconductors are remarkable substances which have zero electrical resistance (perfect conductivity) and expel external magnetic fields (perfect diamagnetism) when cooled below a certain critical temperature.

The project's goal was to investigate how their properties change when the environment has hyperbolic geometry i.e. has non-unique parallel lines through a point, and triangle angle sums are less than 180! Tools from quantum field theory, gauge theory and differential geometry were used to model the hyperbolic superconductors and get mathematical predictions for their properties. It was found that the geometry led to a weaker power decay of an external magnetic field as opposed to the usual flat space exponential decay.

Furthermore, the critical temperature shifted for the infinite volume case - meaning the geometry acted to change electron correlation. This result has the potential to allow better control of superconductor applications like Maglev trains, SQUID detectors and Nuclear Fusion!

**Theme**

Transforming technologies

**Booth**

TT36

**School**

Mathematical Sciences

**Exhibitor**

Ahnaf Tajwar Tahabub