Dr Bea Bleile
Senior Lecturer in Mathematics - School of Science and Technology
Phone: +61 2 6773 3572
Email: bbleile@une.edu.au
Biography
While I enjoyed mathematics at high school, my appreciation of and love for the subject only began to develop during my undergraduate studies at the Swiss Federal Institute of Technology (ETH) in Zurich, where I had enrolled to study physics. I changed to mathematics, completed my Diploma in May 1993 and then took up a three year contract as associate lecturer at UNE.
In 1996 I enrolled for an MSc in homological algebra under the supervision of Peter Hilton to stay in touch with mathematics while caring for our young child. On submitting the Masters thesis in 1999, I enrolled in a PhD in low dimensional algebraic topology under the supervision of Jonathan Hillman at the University of Sydney.
After completing my doctorate in 2005, I spent the academic year 2006-2007 as a post-doctoral fellow at the Institute for Theoretical Physics at ETH, working on the Batalin-Vilkovisky formalism in theoretical physics with Jürg Fröhlich and Carlo Albert. My collaboration with Hans-Joachim Baues on algebraic topology began in 2007 when I was a guest at the Max Planck Institute for Mathematics in Bonn.
Manifolds play an important role in many branches of mathematics and theoretical physics. For example, in general relativity the universe is a 4-dimensional manifold with three spatial dimensions and the fourth dimension given by time. Since many properties of manifolds depend only on the homotopy type of a manifold, that is, they do not change under continuous deformation or homotopy, it has proven fruitful to study Poincaré duality complexes which are homotopy theoretic generalisations of manifolds. These form the main focus of my research.
More recently I started applying algebraic topology in other fields and have been working with Vanessa Robins and others on the persistent homology of digital images.
Qualifications
Dipl Math (ETH Zürich 1993), MSc (UNE 1999), PhD (University of Sydney 2005)
Teaching Areas
I teach undergraduate units in all areas of mathematics as well as honours and postgraduate units in algebraic topology, homological algebra, category theory, differential geometry and topological data analysis.
Research Interests
Manifolds play an important role in many branches of mathematics and theoretical physics. For example, in general relativity the universe is a 4-dimensional manifold with three spatial dimensions and the fourth dimension given by time. Since many properties of manifolds depend only on the homotopy type of a manifold, that is, they do not change under continuous deformation or homotopy, it has proven fruitful to study Poincaré duality complexes which are homotopy theoretic generalisations of manifolds. These form the main focus of my research. More recently I started applying algebraic topology in other fields and have been working with Adélie Garin, Teresa Heiss, Kelly Maggs and Vanessa Robins on the persistent homology of dual digital image constructions.
Research Supervision Experience
Publications
The Persistent Homology of Dual Digital Image Constructions, with Adélie Garin, Teresa Heiss, Kelly Maggs and Vanessa Robins, (2021) https://arxiv.org/abs/2102.11397
Poincaré duality complexes with highly connected universal cover, with Imre Bokor and Jonathan Hillman, Algebraic & Geometric Topology 18, p. 3749–3788 (2018), https://doi.org/10.2140/agt.2008.8.2355
The third homotopy group as a pi1-module, with Hans-Joachim Baues Applicable Algebra in Engineering, Communication and Computing, v. 26 (1-2), p. 165-189 (2015), https://doi.org/10.1007/s00200-014-0240-5
Batalin-Vilkovisky integrals in finite dimensions, with Juerg Froehlich and Carlo Albert Journal of Mathematical Physics, v. 51 (1), p. 1-31 (2010) https://doi.org/10.1063/1.3278524
Poincaré duality complexes in dimension four, with Hans-Joachim Baues Algebraic and Geometric Topology, v. 8, p. 2355-2389 (2008) , https://doi.org/10.2140/agt.2008.8.2355
Memberships
Australian Mathematical Society, Australian and New Zealand Association of Mathematical Physics, American Mathematical Society, ETH Alumni
