Jessica Purcell: Triangulations, geometry and knots

In this research profile, upcoming SMRI visitor Jessica Purcell describes the open questions in the study of 3-manifolds and how her fascination with mathematical knots began.

Jessica Purcell is a Professor in the School of Mathematical Sciences and Associate Dean of Research (Faculty of Science) at Monash University, where she carries out research into 3-manifolds, hyperbolic geometry and knot theory.

Professor Purcell will visit SMRI as part of the Domestic Visitor Program in late 2021.Together with her University of Sydney collaborator Professor Stephan Tillmann, the mathematicians will investigate minimal triangulations of 3-manifolds, an area with important applications in computational and quantum topology.

'Hyperbolic Knot Theory' by Jessica S. Purcell: Monash University, available at:

Papers referenced:

Purcell 2008, Cusp shapes under cone deformation, J. Differential Geom. 80(3): 453-500. DOI: 10.4310/jdg/1226090484

Van Wijk, Jarke J. and Arjeh M. Cohen. 2006, Visualization of Seifert Surfaces, IEEE Trans. on Visualization and Computer Graphics, 12(4,) 485-496.

Cooper, Lackenby & Purcell 2008, The length of unknotting tunnels, Algebr. Geom. Topol. 10 (2010) 637-661. 10.2140/agt.2010.10.637

Dang & Purcell 2019 Cusp shape and tunnel number, P,roc. Ameri. Math. Society 147, 1351-1366

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