Jessica Purcell is a Professor of Mathematics in the School of Mathematics at Monash University.
Jessica's research is in geometry and topology. She works on problems in the overlap of hyperbolic geometry, 3-manifolds, and knot theory. She obtained a PhD in Mathematics from Stanford University, held postdoctoral positions at the University of Texas in Austin and the University of Oxford, and worked at Brigham Young University from 2007 to 2015. She arrived at Monash in 2015.
At Monash, Jessica's research is currently supported by funding from the Australian Research Council (ARC). She was an ARC Future Fellow from 2017 to 2021. Prior to that, she was a Von Neumann Fellow at the Institute for Advanced Study (2015), a Sloan Research Fellow (2011), and held a CAREER award from the National Science Foundation of the USA (2013-2015).
For more details, please see Jessica's brief curriculum vita.
Qualifications
PhD Mathematics, Stanford University, 2004
Thesis: Cusp shapes of Hyperbolic link complements and Dehn filling, supervised by Steven Kerckhoff.
MS Mathematics, University of Michigan, 1999
BA Mathematics, University of Utah, 1998
Minor in Computer Science
Summa cum laude
Positions
I have worked as a research mathematician on three continents, and have had the opportunity to work with outstanding researchers across the world.
Professor, School of Mathematics, Monash University (Jan 2019-)
Deputy Dean (Research), Monash University Faculty of Science (Nov 2020 - Dec 2023). I worked with an interdisciplinary team to enable and build up research in five different schools in Monash Science.
Associate Professor, School of Mathematics, Monash University (Aug 2015 - Dec 2018)
Von Neumann Fellow, Institute for Advanced Study (IAS), Princeton (Sep 2015 - Dec 2015)
Associate Professor, Mathematics Department, Brigham Young University (Sep 2013 - Jul 2015)
Visiting Academic, School of Mathematics and Statistics, University of Melbourne (Jan 2014 - Aug 2014)
Assistant Professor, Mathematics Department, Brigham Young University (Jun 2007 - Sep 2013)
Postdoctoral Researcher, University of Oxford Mathematical Institute (Sep 2007 - Sep 2008)
Instructor and VIGRE Instructor (Postdoctoral), Mathematics Department, University of Texas at Austin (Sep 2004 - Jun 2007)
Awards
Fellow of the Australian Academy of Science (2025)
Fellow of the American Mathematical Society (2025)
Fellow of the Australian Mathematical Society (2025)
Maureen Brunt Fellowship (2023 - 2025). Monash University fellowship supporting senior women academics.
Australian Research Council Future Fellowship (2017 - 2021). Fellowship to support mid-career researchers.
Von Neumann Fellow, Institute for Advanced Study (IAS) (2015). Fellowship to support mid-career researchers visiting the IAS.
National Science Foundation Career Award (2013 - 2015). To support early career researchers.
Sloan Research Fellow (2011). To support early career researchers.
Leadership and Engagement in Mathematics
Mathematics should be inclusive and diverse. People from all backgrounds can and do appreciate mathematics, given encouragement and opportunities. Through my contributions to the mathematical community, I seek to provide this encouragement and these opportunities.
President of the Australian Mathematical Society (Dec 2022 - Dec 2024)
President elect (Dec 2021 - Dec 2022)
Outgoing President (Dec 2024 - Dec 2025)
Chair of Women in Mathematics Special Interest Group (WIMSIG) of the Australian Mathematical Society (Jan 2019 - Jan 2021)
Incoming Chair (Jan 2018 - Jan 2019)
Immediate Past Chair (Jan 2021 - Jan 2022)
Editorial board member of Transactions of the London Mathematical Society (Jan 2021-)
Editorial board member Algebraic and Geometric Topology (Sep 2023 -)
Organiser of research seminars in mathematics (2008-)
Australian Geometric Topology Webinar (Mar 2020 - 2023)
Monash Topology Seminar (Jan 2016-2019)
Brigham Young University Topology Seminar (Sep 2008-Apr 2015)
Organiser of research conferences in mathematics (2009-)
Dynamics, Foliations, and Geometry II. Hybrid workshop in Creswick, Victoria, Australia and Regensburg, Germany (Feb 2022)
WIMSIG 2021: A Celebration of Women in Mathematical and Statistical Sciences. This was run in hub format: in-person at hubs in Brisbane, Perth, Adelaide, and Hobart, and online in Melbourne and Sydney. (Oct 2021)
MATRIX-MFO Tandem Workshop on Invariants and Structures in Low-Dimensional Topology. Hybrid conference, run in-person at MFO Oberwolfach in Germany, and online at the Matrix Centre in Australia (Sep 2021)
Low-Dimensional Topology. Oberwolfach, Germany. (Feb 2020)
Classical and quantum 3-manifold topology. Monash University. (Dec 2018)
Geometry and Topology of 3-Manifolds. Okinawa Institute of Science and Technology, Okinawa, Japan (May 2018)
Workshop on low-dimensional topology and quantum algebra, Australian National University, Canberra, Australia (Nov 2016)
Moab Topology Conferences: 2015, 2012, 2009.
Geometric Topology in Cortona, Cortona, Italy (Jun 2013)
Rigidity and Flexibility in Dimensions 2, 3, and 4, in honor of Steven Kerckhoff. Luminy, France (May 2012)
Research Publications
I have written over fifty research papers on knot theory, hyperbolic geometry, and 3-manifolds. All appear in strong peer-reviewed journals or conference proceedings. I have also written two books: a research monograph and a text for graduate students.
Research overview and publications: See research page
Graduate text Hyperbolic Knot Theory