Available student project - Combinatorics and integrable systems

Research fields

  • Theoretical Physics

Project details

During last decades integrable systems helped to answer a number of difficult outstanding questions in mathematics. They led to advances in knot theory, string theory, theory of differential equations, etc. This project consider connections of integrable systems to combinatorial problems and special functions. It is natural to consider quantum spins systems with discrete fluctuating variables  as an efficient tool to count ``something" in its configuration space of the system. For example, we can talk about the total number of configurations with 11 spins up, etc. Recently it was found that one can count some special types of matrices using such techniques. It led to a large boost of interest which helped to prove many conjectures in the theory of alternating sign matrices.This project aims to look at different generalizations of such connections.

Required background

PHYS2020, MATH2406, MATH3351

Project suitability

This research project can be tailored to suit students of the following type(s)
  • 3rd year special project
  • PhB (2nd or 3rd year)
  • Honours or MSc project
  • Phd or MPhil

Contact supervisor

Mangazeev, Vladimir profile

Other supervisor(s)

Bazhanov, Vladimir profile

Updated:  8 February 2023/ Responsible Officer:  Director, RSPhys/ Page Contact:  Physics Webmaster