Research

 
 

My papers on the arXiv


Recent & Coming Events:

Workshop on Low-Dimensional Topology and Quantum Algebra (ANU, 31 October - 4 November)

2016 AustMS Meeting (ANU, 5 - 8 December)

I'm co-organising the Topology Session. Please email me for details!

AMSI Winter School (University of Queensland, 29 June - 10 July, 2015)

I taught a course on moduli spaces in symplectic geometry with Brett Parker.


Some past talks:

BIRS (2014) click here.

MSRI (2010) click here.


Collaborators:

Nathan Dunfield

David Gay

Neil Hoffman

Umberto Hryniewicz

Josh Sabloff

Umberto Salamao






   

My research focuses on knots and three-manifolds.  I am particularly interested in the Floer-theoretic tools of Heegaard Floer theory and Legendrian contact homology.  Both of these are defined via pseudo-holomorphic curves in symplectic manifolds, but they can be approached from a combinatorial perspective as well.  Generally speaking, the geometric theories are more powerful while the combinatorial versions are easier to work with.  I study the interplay between these two viewpoints, as well as their applications to topological and geometric questions.  In addition to contact geometry, I am also interested in topological topics such as Dehn surgery, Heegaard splittings, and link genus.