David Baraglia

Dr David Baraglia

Senior Lecturer

School of Mathematical Sciences

College of Science

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

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 - ongoing Senior Lecturer University of Adelaide, Adelaide
2016 - ongoing 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
2024 Baraglia, D., & Hekmati, P. (2024). Equivariant Seiberg-Witten-Floer cohomology. Algebraic and Geometric Topology, 24(1), 493-554.
DOI Scopus4 WoS2
2024 Baraglia, D. (2024). Knot concordance invariants from Seiberg–Witten theory and slice genus bounds in 4-manifolds. International Journal of Mathematics, 35(10), 29 pages.
DOI
2024 Baraglia, D., & Hekmati, P. (2024). Brieskorn spheres, cyclic group actions and the Milnor conjecture. Journal of Topology, 17(2), 40 pages.
DOI
2024 Baraglia, D. (2024). An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds. Mathematical Research Letters, 31(2), 329-352.
DOI
2023 Baraglia, D. (2023). Non-trivial smooth families of K3 surfaces. Mathematische Annalen, 387(3-4), 1719-1744.
DOI Scopus2 WoS1
2023 Baraglia, D. (2023). Tautological classes of definite 4-manifolds. Geometry and Topology, 27(2), 641-698.
DOI Scopus1
2023 Baraglia, D., & Konno, H. (2023). A note on the Nielsen realization problem for K3 surfaces. Proceedings of the American Mathematical Society, 151(9), 4079-4087.
DOI Scopus12 WoS11
2023 Baraglia, D. (2023). On the slice genus of quasipositive knots in indefinite 4-manifolds. Selecta Mathematica, New Series, 29(4), 12 pages.
DOI
2022 Baraglia, D., & Konno, H. (2022). On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds. Journal of Topology, 15(2), 505-586.
DOI Scopus11 WoS10
2022 Baraglia, D., & Hekmati, P. (2022). A foliated Hitchin-Kobayashi correspondence. Advances in Mathematics, 408, 108661-1-108661-47.
DOI Scopus6 WoS5
2021 Baraglia, D. (2021). Constraints on families of smooth 4–manifolds from bauer–furuta invariants. Algebraic and Geometric Topology, 21(1), 317-349.
DOI Scopus13 WoS12
2020 Baraglia, D., & Konno, H. (2020). A gluing formula for families Seiberg–Witten invariants. Geometry and Topology, 24(3), 1381-1456.
DOI Scopus18 WoS16
2019 Mathai, V., Thiang, G. C., Hekmati, P., Bursztyn, H., Bouwknegt, P., & Baraglia, D. (2019). Foreword: String geometries, dualities and topological matter. Journal of Geometry and Physics, 138, 331-332.
DOI
2019 Baraglia, D., & Schaposnik, L. P. (2019). Cayley and Langlands type correspondences for orthogonal Higgs bundles. Transactions of the American Mathematical Society, 371(10), 7451-7492.
DOI Scopus10 WoS9
2019 Baraglia, D. (2019). Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory. Advances in Mathematics, 354, 32 pages.
DOI Scopus11 WoS11
2019 Baraglia, D., Kamgarpour, M., & Varma, R. (2019). Complete Integrability of the Parahoric Hitchin System. International Mathematics Research Notices, 2019(21), 6499-6528.
DOI Scopus11 WoS9
2019 Baraglia, D., & Huang, Z. (2019). Special Kähler geometry of the Hitchin system and topological recursion. Advances in Theoretical and Mathematical Physics, 23(8), 1981-2024.
DOI Scopus6 WoS6
2018 Baraglia, D., & Kamgarpour, M. (2018). On the image of the parabolic Hitchin map. Quarterly Journal of Mathematics, 69(2), 681-708.
DOI Scopus10 WoS9
2018 Baraglia, D. (2018). Monodromy of the SL(n) and GL(n) Hitchin fibrations. Mathematische Annalen, 370(3-4), 1681-1716.
DOI Scopus3 WoS3
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 Scopus14 WoS10
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 Scopus18 WoS15
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 Scopus3 WoS3
2016 Baraglia, D., & Hekmati, P. (2016). Moduli spaces of contact instantons. Advances in Mathematics, 294, 562-595.
DOI Scopus8 WoS8
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 Scopus11 WoS12
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 Scopus39 WoS35
2015 Baraglia, D. (2015). Topological T-duality for torus bundles with monodromy. Reviews in Mathematical Physics, 27(3), 1550008-1-1550008-55.
DOI Scopus5 WoS4
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 Scopus43 WoS41
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 Scopus3 WoS3
2015 Baraglia, D. (2015). Cyclic Higgs bundles and the affine Toda equations. Geometriae Dedicata, 174(1), 25-42.
DOI Scopus22 WoS21
2014 Baraglia, D. (2014). Topological T-duality for general circle bundles. Pure and Applied Mathematics Quarterly, 10(3), 367-438.
DOI Scopus12 WoS10
2014 Baraglia, D. (2014). Variation of Hodge structure for generalized complex manifolds. Differential Geometry and its Application, 36, 98-133.
DOI Scopus2 WoS1
2014 Baraglia, D., & Schaposnik, L. (2014). Higgs bundles and (A, B, A)-branes. Communications in Mathematical Physics, 331(3), 1271-1300.
DOI Scopus36 WoS30
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 Scopus12 WoS10
2012 Baraglia, D. (2012). Leibniz algebroids, twistings and exceptional generalized geometry. Journal of Geometry and Physics, 62(5), 903-934.
DOI Scopus56 WoS55
2010 Baraglia, D. (2010). Moduli of coassociative submanifolds and semi-flat G2-manifolds. Journal of Geometry and Physics, 60(12), 1903-1918.
DOI Scopus13 WoS12

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.
DOI
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).

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

Date Role Research Topic Program Degree Type Student Load Student Name
2025 Co-Supervisor Holomorphic flexibility properties of character varieties and related moduli spaces Doctor of Philosophy Doctorate Full Time Mr Stefano Giannini
2024 Principal Supervisor Cohomology Rings of Topological and Smooth 4-Manifolds Master of Philosophy Master Full Time Mr Paawan Nileshkumar Jethva
2024 Principal Supervisor Real Seiberg-Witten invariants of complex 4-manifolds Doctor of Philosophy Doctorate Full Time Mr Junjie Chong
2023 Principal Supervisor K-Theory of Topological Insulators Doctor of Philosophy Doctorate Full Time Mr Joshua Celeste

Date Role Research Topic Program Degree Type Student Load Student Name
2023 - 2025 Principal Supervisor On the Classification of Enriques Surfaces Master of Philosophy Master Full Time Mr Radee Stefanov Tchorbadjiev
2022 - 2025 Principal Supervisor A Connected Sum Formula for the Seiberg-Witten Invariant of 4-Manifold Families Doctor of Philosophy Doctorate Full Time Mr Joshua Rikihana John Tomlin
2022 - 2025 Co-Supervisor Dense Entire Curves in Spaces of Holomorphic Maps Master of Philosophy Master Full Time Mr Tyson Jack Rowe
2021 - 2023 Principal Supervisor Langlands Duality in the Generic Fibres of Classical Hitchin Fibrations Master of Philosophy Master Full Time Mr Tyson Joel Klingner
2021 - 2023 Co-Supervisor The Closing Lemma for Riemann Surfaces Master of Philosophy Master Full Time Mr Wills Ton Minh Nguyen
2020 - 2022 Principal Supervisor The families Seiberg-Witten invariants of smooth families of Kahler surfaces Master of Philosophy Master Full Time Mr Joshua Celeste
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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