A cluster diagram is a combinatorial object that can be associated to a polynomial which encodes a lot or relevant arithmetic information about the polynomial. The goal of this project is to learn about these diagrams, and the information that can be extracted from them. In particular, you will explore what the Cluster diagram of a polynomial f(x) can tell you about the fields of definition of solutions to equations of the form y^n = f(x).
Supervisors
Primary Supervisor: Brendan Creutz
Key qualifications and skills
Required: MATH321 or good knowledge of groups and fields.
Desired: MATH411 (Galois Theory) and some experience coding (e.g., Python or Sage)
Does the project come with funding
No - Student must be self-funded
Final date for receiving applications
Ongoing
How to apply
Direct inquiries to brendan.creutz@canterbury.ac.nz
Keywords
Number Theory, Algebraic Geometry
