Cluster algebras and Teichmuller theory
Lead Research Organisation:
Durham University
Department Name: Mathematical Sciences
Abstract
Cluster algebras is a relatively new field in mathematics (first introduced and studied by Fomin and Zelevinsky in 2002) which turned out to be connected to many classical fields.
The aim of the current project is to explore various connections between the theory of cluster algebras and Teichmuller theory.
The aim of the current project is to explore various connections between the theory of cluster algebras and Teichmuller theory.
Organisations
People |
ORCID iD |
| Anna Felikson (Primary Supervisor) | |
| John Blackman (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509462/1 | 01/10/2016 | 30/09/2021 | |||
| 1735520 | Studentship | EP/N509462/1 | 01/10/2016 | 31/03/2020 | John Blackman |
| Description | Over the course of this project, I have investigated integer multiplication of continued fractions using geometric structures. In particular, I have shown that integer multiplication of a continued fraction can be represented by replacing one triangulation of a surface with another triangulation. This method can be used to show that eventually recurrent continued fractions have partial quotients which have exponential growth when iteratively multiplied by n, for n any fixed, natural number. |
| Exploitation Route | This work could be used to help develop the theory surrounding the p-adic Littlewood Conjecture. |
| Sectors | Other |
| URL | https://arxiv.org/abs/1809.09670 |