Finn is a third-year science major at Melbourne University. He is currently completing a major in mathematics and statics with a specialisation in pure mathematics. Finn’s mathematical interests vary across a wide range of specialisations. He enjoys learning ideas from the more abstract areas of pure mathematics such as category theory and algebra, however he is also interested in applications to physics and the world of probability theory. Finn’s interests outside of mathematics include eating pasta and playing the bass.
Notes on alcove path models and affine Springer fibres
Refined alcove path models are a recent development in combinatorial representation theory, I propose to apply these models to attempt to study the combinatorics of the affine Springer fibre in the case of the special linear group. This is work based on Arun Ram’s refined alcove path model for the affine flag varieties. I have been attending a series in which Arun has explained these models, and I hope to use the AMSI program as an opportunity to build upon his work.