Mathematical Aspects of Conformal Field Theory
operator theoretic aspects of quantum field theory
computational problems in vector-valued modular forms
tensor categories and functorial conformal field theories
I am available to supervise Honours, Masters, and PhD projects on a variety of mathematical topics connected to conformal field theory. All projects will emphasize mathematical rigour, and it is not a requirement that all projects explicitly connect to mathematical physics. Honorus and Masters projects will generally be either algebraic or analytic in nature, whereas PhD projects will often blend algebraic and analytic aspects.
Typical background expectations are:
- Honours and Masters projects: advanced coursework in analysis (for analysis focused theses) or advanced coursework in algebra (for algebra focused theses). In terms of ANU courses, for an analysis thesis this could mean a strong result in Analysis 2, with Analysis 3, Complex Analysis, and/or relevant special topics courses desirable. For an algebra thesis, some options for advanced coursework could be the represenation theory ASE with Algebra 1 along with Algebra 2, Topics in Mathematical Physics, and/or relevant special topics courses.
- PhD projects: all projects will be mathematics theses, with the option of having motivation from physics. A strong background in mathematics is necessary, and students are expect to have a strong foundation in analysis, algebra, and other relevant mathematical fundamentals. Students will generally be expected to have completed a mathematics Honours or Masters project related to the proposed PhD topic (although in some circumstances direct entry from an international bachelor's program may be possible).
These requirements are a guideline; please feel free to contact me to discuss your specific circumstances.
Some broad areas that a project could connect to are listed below (but don't worry if you haven't heard of any of these things!). Please enquire with me if you would like to discuss project possibilities.
- theory of operator algebras (analysis)
- operator theoretic aspects of quantum field theory (analysis)
- representation theory of vertex operator algebras (algebra)
- computational problems in vector-valued modular forms (algebra)
- tensor categories and functorial conformal field theories (algebra)
I am also available for reading courses or special topics courses. Some potential courses topics include operator aglebras (e.g. C* and/or von Neumann algebras) and various topics related to the mathematics of conformal field theory (e.g. foundations of CFT, representation theory of loop groups, and/or monstrous moonshine).