The affine nilTemperley-Lieb algebra and its action on particle configurations

The affine nilTemperley-Lieb algebra can be characterised by its faithful action on fermionic particle configurations on a circle. This action allows for a nice visualisation, and furthermore, one can use it to derive several properties of the affine nilTemperley-Lieb algebra, including an explicit description of its centre and a classification of its simple modules. This talk is based on joint work with G. Benkart and the speaker's PhD thesis.