School of Mathematical Sciences
Faculty of Engineering, Computer and Mathematical Sciences
Eligible to supervise Masters and PhD - email supervisor to discuss availability.
- My Research
- Grants and Funding
- Professional Activities
Differential geometry, complex geometry, gauge theory and mathematics physics. Particularly the study of moduli spaces of geometric structures on manifolds such as:
- Applications of gauge theory to the study of 4-manifolds, including group actions and families of 4-manifolds.
- Moduli spaces of Higgs bundles and holomorphic vector bundles, character varieties and connections to the Geometric Langlands Program.
- Gauge theoretic moduli spaces in various dimensions, such as Seiberg-Witten theory, Yang-Mills connections and gauge theory on foliated spaces.
Mathematical physics, particularly geometric aspects of quantum field theory and string theory including T-duality and twisted K-theory.
Date Position Institution name 2018 Senior Lecturer University of Adelaide, Adelaide 2016 DECRA Fellow University of Adelaide, Adelaide 2012 - 2017 Lecturer University of Adelaide, Adelaide 2012 - 2015 Australian Postdoctoral Fellow (APD) University of Adelaide, Adelaide 2011 - 2012 Australian Postdoctoral Fellow (APD) Australian National University, Canberra 2010 - 2011 Research Associate Australian National University, Canberra
Date Institution name Country Title — University of Oxford, Oxford United Kingdom PhD — University of Adelaide, Adelaide Australia Masters by Research — University of Adelaide, Adelaide Australia B. Eng, Electrical and Electronic, 1st Class Honours with B. Math and Comp Sci, 1st Class Honours
Year Citation 2018 Baraglia, D., Biswas, I., & Schaposnik, L. (2018). Brauer group of Moduli of Higgs bundles and connections. In A. Dancer, J. Andersen, & O. Garcia-Prada (Eds.), Geometry and Physics: A Festschrift in Honour of Nigel Hitchin (Vol. 2, pp. 387-398). United Kingdom: Oxford University Press.
2013 Baraglia, D. P. (2013). Introduction to Generalized Geometry and T-duality. In L. Ji, Y. -S. Poon, & S. -T. Yau (Eds.), Open Problems and Surveys of Contemporary Mathematics (pp. 45-97).
- Associate Investigator on Marsden Fund Grant (with Principal Investigator P. Hekmati), Exploiting gauge theory and duality in geometry, $345,000 (NZD) (2017).
- Australian Research Council Discovery Project (with V. Mathai), Parametrised gauge theory and positive scalar curvature, 3 year project, $335,000 (2016).
- Australian Research Council Discovery Early Career Researcher Award (DECRA) Higgs bundle moduli spaces and spectral data, 3 year project, $396,104 (2015).
- Faculty research grant, New applications of Gauge Theory to Geometry, $16,500 (2014).
- Start-up funding, $10,000 over 18 months (2012).
- Australian Research Council Australian Postdoctoral Fellowship (APD), Applications of generalised geometry to duality in quantum theory, 3 year project, $285,000 (2010).
- 2017 Algebraic Topology - honours course
- 2016 Maths IB algebra
- 2016 Introduction to Financial Mathematics I
- 2015 Maths IB calculus
- 2015 Groups and Rings III
- 2014 Maths IB linear algebra
- 2013 Algebraic Topology - honours course
- 2012 Applications of Quantitative Methods in Finance I
- 2012 Fields and Modules III
- 2011 Algebraic Topology - honours course (ANU)
- 2018 Masters student Ahnaf Tajwar Tahabub (co-supervised with V. Mathai)
- 2017 Masters student John McCarthay (co-supervised with V. Mathai)
- 2016 Summer research student Jake Miell
- 2016 Masters student Michael Hallam (co-supervised with V. Mathai)
- 2015 PhD student Zhenxi Huang (co-supervised with V. Mathai)
- 2013 Honours student Thi Quynh Trang Nguyen. Thesis: Einstein Metrics on Principal Circle Bundles
- 2011 Summer reading course for honours student - Kahler manifolds (ANU)
- 2018 Intermediate notions - graduate student seminar
- 2016 - 2015 Basic notions - graduate student seminar
- 2014 - 2015 Strings journal club - research seminar
Current Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2021 Co-Supervisor Properties of the Spectra of an Infinite Random Cayley Graph Master of Philosophy Master Full Time Mr Matthias Eduard Fresacher 2021 Principal Supervisor Moduli spaces of parahoric Higgs bundles and Langlands duality Master of Philosophy Master Full Time Mr Tyson Joel Klingner 2020 Principal Supervisor Invariants of Families of 4-Manifolds Master of Philosophy Master Full Time Mr Joshua Celeste 2020 Co-Supervisor Further Developments of Geometric Methods motivated by Condensed Matter Physics Doctor of Philosophy Doctorate Full Time Ms Marisa Christin Schult
Past Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2017 - 2018 Co-Supervisor Hitchin's Projectively Flat Connection and the Moduli Space of Higgs Bundles Master of Philosophy Master Full Time Mr John Benjamin McCarthy 2016 - 2018 Co-Supervisor Generalised Eta Invariants, End-Periodic Manifolds, and their Applications to Positive Scalar Curvature Master of Philosophy Master Full Time Mr Michael Hallam 2015 - 2018 Co-Supervisor Metrics and Special Kähler Geometry on the Moduli Spaces of Higgs Bundles and Hitchin Systems Doctor of Philosophy Doctorate Full Time Mr Zhenxi Huang
Date Role Membership Country 2015 - ongoing Member Australian Mathematical Society Australia
Date Role Editorial Board Name Institution Country 2017 - ongoing Editor Journal of Geometry and Physics special issue: String geometries, dualities and topological matter Elsevier Netherlands
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