Research Interests
 Conformal field theory
 Vertex operator algebras
 Representation theory
 Lie (super) algebras
 Integrable models
Research Groups
Publications
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Extra Information
I study the mathematical structures that underlie my favourite physical theories. These include vertex operator algebras / conformal field theories and their relations with string theory, integrable models, representation theory and number theory (and anything else that I can think of). At the moment, this means logarithmic conformal field theory, KacMoody superalgebras, nonsemisimple tensor categories and mock modular forms. I'm especially interested in the appearance of indecomposable (but reducible) representations in physics, but pretty much anything that involves cool math is fine with me.
Currently, I'm studying examples of conformal field theories in which the correlation functions exhibit logarithmic singularities. In representationtheoretic terms, these logarithmic theories are built from representations which are indecomposable but not irreducible. Such theories arise naturally when considering socalled nonlocal observables (crossing probabilities, fractal dimensions) in the conformal limit of many exactly solvable lattice models (percolation, Ising). They are also relevant to stringtheoretic considerations, especially when the target space admits fermionic directions, AdS/CFT, and perhaps even to black hole holography.
In mathematics, there is a tantalising suggestion that logarithmic conformal field theory and SchrammLoewner Evolution may be equivalent in some sense. The corresponding logarithmic vertex operator algebras also suggest natural generalisations of the notion of a modular tensor category. Finally, the characters of the modules of a vertex operator algebra tend to have nice modular properties. Some of the examples that I study are related to false / partial theta functions and mock / quantum modular forms.
Current Postgraduate Supervision
Name 
Thesis title 
Zachary FEHILY 

Past Postgraduate Supervision
Name 
Thesis title 
Tianshu LIU 
"Coset construction for the N=2 and osp(1/2) minimal models" 
Steve SIU 
"Singular vectors for the WN algebras and the BRST cohomology for relaxed highestweight Lk(sl(2)) modules" 
Current MSc Students
Name 
Project title 
Tyson FIELD 

Daniel TAN 
"to be confirmed" 
Past Honours & MSc Students
Name 
Project title 
Benjamin GERRATY 

William STEWART 

Recent Grant History
Year(s) 
Source 
Type 
Title 
2020  2023 
ARC 
Future Fellow 
Logarithmic conformal field theory and the 4D/2D correspondence 
2016  2018 
ARC 
Discovery 
Towards higher rank logarithmic conformal field theories 
2010  2014 
ARC 
Discovery 
Indecomposable structure in representation theory and logarithmic conformal field theory 
Responsibilities
 BSc Mathematics & Statistics Major Coordinator
 Course advisors  Upper Undergraduate
Committees
 Executive Committee
 Management Committee
 Postgraduate Programs Committee