Ainsley Nicoll
Diagram Bethe ansatz
The Markov generator of the asymmetric exclusion process as well as the Hamiltonian of the quantum XXZ spin-chain can both be realised via a representation of the Temperley-Lieb algebra. In this project I will familiarise myself with the Temperley-Lieb algebra and Bethe ansatz techniques and recent tensor product approaches to diagonalise this Hamiltonian in a universal algebraic setting. The primary research question will be whether this diagonalisation can be extended above the current constraint cases into more general solutions.
Ainsley Nicoll
The University of Melbourne
Ainsley is a final year student at the University of Melbourne, majoring in pure mathematics. His interests in mathematics are broad, however he has a particular leaning towards mathematical physics, enjoying its ability to draw on a great breadth of mathematical ideas in solving problems. Ainsley has previously undertaken a project in physical combinatorics and he is excited to see more of what research has to offer.
In his spare time, Ainsley enjoys helping out on the committee of the universities’ Mathematics and Statistics Society as well as participating in volunteer tutoring for high school students.
