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Dr David Baraglia

David Baraglia
Senior Lecturer
School of Mathematical Sciences
Faculty of Engineering, Computer and Mathematical Sciences

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External Profiles

Dr David Baraglia

Eligible to supervise Masters and PhD — email supervisor to discuss availability.

Differential geometry, gauge theory and mathematics physics. Particularly the study of moduli spaces of geometric structures on manifolds such as:

  • Higgs bundle moduli spaces and character varieties.
  • Gauge theoretical moduli spaces in various dimensions, such as the moduli space of contact instantons on contact 5-manifolds and gauge theory on foliated spaces.

Mathematical physics, particularly geometric aspects of quantum field theory and string theory including:

  • Generalised geometry, T-duality and twisted K-theory.

Appointments

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

Education

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

Journals

Year Citation
2018 Baraglia, D. (2018). Monodromy of the SL(n) and GL(n) Hitchin fibrations. Mathematische Annalen, 370(3-4), 1681-1716.
DOI
2018 Baraglia, D., & Schaposnik, L. (2018). Monodromy of rank 2 twisted hitchin systems and real character varieties. Transactions of the American Mathematical Society, 370(8), 5491-5534.
DOI Scopus2
2018 Mathai, V., Thiang, G., Hekmati, P., Bursztyn, H., Bouwknegt, P., & Baraglia, D. (2018). Foreword: String geometries, dualities and topological matter. Journal of Geometry and Physics.
DOI
2018 Baraglia, D., & Kamgarpour, M. (2018). On the image of the parabolic Hitchin map. Quarterly Journal of Mathematics, 69(2), 681-708.
DOI
2017 Baraglia, D., & Hekmati, P. (2017). Arithmetic of singular character varieties and their E-polynomials. Proceedings of the London Mathematical Society, 114(2), 293-332.
DOI Scopus1 WoS1
2016 Baraglia, D., Biswas, I., & Schaposnik, L. (2016). Automorphisms of ℂ* moduli spaces associated to a Riemann surface. Symmetry, Integrability and Geometry : Methods and Applications, 12, 007-1-007-14.
DOI Scopus1 WoS2
2016 Baraglia, D., & Hekmati, P. (2016). Moduli spaces of contact instantons. Advances in Mathematics, 294, 562-595.
DOI Scopus2 WoS2
2016 Baraglia, D. (2016). Classification of the automorphism and isometry groups of Higgs bundle moduli spaces. Proceedings of the London Mathematical Society, 112(5), 827-854.
DOI Scopus1 WoS1
2016 Baraglia, D., & Schaposnik, L. (2016). Real structures on moduli spaces of Higgs bundles. Advances in Theoretical and Mathematical Physics, 20(3), 525-551.
DOI Scopus5 WoS4
2015 Baraglia, D., & Hekmati, P. (2015). A Fourier-Mukai approach to the K-theory of compact Lie groups. Advances in Mathematics, 269, 335-345.
DOI
2015 Baraglia, D. (2015). Cyclic Higgs bundles and the affine Toda equations. Geometriae Dedicata, 174(1), 25-42.
DOI Scopus3 WoS3
2015 Baraglia, D. (2015). Topological T-duality for torus bundles with monodromy. Reviews in Mathematical Physics, 27(3), 1550008-1-1550008-55.
DOI Scopus1 WoS1
2015 Baraglia, D., & Hekmati, P. (2015). Transitive Courant algebroids, string structures and T-duality. Advances in Theoretical and Mathematical Physics, 19(3), 613-672.
DOI Scopus10 WoS11
2014 Baraglia, D. (2014). Topological T-duality for general circle bundles. Pure and Applied Mathematics Quarterly, 10(3), 367-438.
DOI Scopus5 WoS4
2014 Baraglia, D. (2014). Variation of Hodge structure for generalized complex manifolds. Differential Geometry and its Application, 36, 98-133.
DOI Scopus1 WoS1
2014 Baraglia, D., & Schaposnik, L. (2014). Higgs bundles and (A, B, A)-branes. Communications in Mathematical Physics, 331(3), 1271-1300.
DOI Scopus13 WoS9
2014 Baraglia, D. (2014). A coboundary morphism for the grothendieck spectral sequence. Applied Categorical Structures, 22(1), 269-288.
DOI Scopus1 WoS1
2013 Baraglia, D. (2013). Conformal courant algebroids and orientifold T-duality. International Journal of Geometric Methods in Modern Physics, 10(2), 1-35.
DOI Scopus2 WoS2
2012 Baraglia, D. (2012). Leibniz algebroids, twistings and exceptional generalized geometry. Journal of Geometry and Physics, 62(5), 903-934.
DOI Scopus31 WoS31
2010 Baraglia, D. (2010). Moduli of coassociative submanifolds and semi-flat G2-manifolds. Journal of Geometry and Physics, 60(12), 1903-1918.
DOI Scopus1 WoS1

Book Chapters

Year Citation
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).

Conference Papers

  • 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).

Lecturing

  • 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)

Student supervision

  • 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)

Seminar organisation

  • 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
2018 Co-Supervisor Seibert-Witten Equations and Pseudo-holomorphic Curves Applied to Superconductors and Particle Physics Master of Philosophy Master Full Time Mr Ahnaf Tajwar Tahabub
2015 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

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

Memberships

Date Role Membership Country
2015 - ongoing Member Australian Mathematical Society Australia

Editorial Boards

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
Position
Senior Lecturer
Phone
83131604
Fax
8313 3696
Campus
North Terrace
Building
Ingkarni Wardli, floor 6
Room Number
6 57
Org Unit
Mathematical Sciences

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