Nicholas Buchdahl

• Journals

  Year	Citation
  2023	Buchdahl, N., & Schumacher, G. (2023). Weil-Petersson forms for families of polystable bundles over compact Kähler manifolds. International Journal of Mathematics, 34(13), 28 pages. DOI
  2022	Buchdahl, N., & Schumacher, G. (2022). Polystable bundles and representations of their automorphisms. Complex Manifolds, 9(1), 78-113. DOI Scopus2
  2022	Buchdahl, N., & Schumacher, G. (2022). An analytic application of Geometric Invariant Theory II: Coarse moduli spaces. Journal of Geometry and Physics, 175, 104467. DOI Scopus2
  2021	Buchdahl, N., & Schumacher, G. (2021). An analytic application of Geometric Invariant Theory. Journal of Geometry and Physics, 165, 104237. DOI Scopus3
  2021	Alagumalai, S., & Buchdahl, N. (2021). PISA 2012: Examining the influence of prior knowledge, time-on-task, school-level effects on achievements in mathematical literacy processes – Interpret, employ and formulate. Australian Journal of Education, 65(2), 173-194. DOI Scopus3 WoS1
  2020	BUCHDAHL, N. P., & SCHUMACHER, G. (2020). L2-cohomology for affine spaces and an application to monads. Rocky Mountain Journal of Mathematics, 50(5), 1599-1616. DOI
  2020	Buchdahl, N., & Schumacher, G. (2020). Polystability and the Hitchin-Kobayashi correspondence.
  2018	Buchdahl, N., Teleman, A., & Toma, M. (2018). On the Donaldson–Uhlenbeck compactification of instanton moduli spaces on class VII surfaces. Quarterly Journal of Mathematics, 69(4), 995-1028. DOI Scopus1
  2017	Buchdahl, N., Teleman, A., & Toma, M. (2017). A continuity theorem for families of sheaves on complex surfaces. Journal of Topology, 10(4), 995-1028. DOI Scopus7
  2008	Buchdahl, N. (2008). Algebraic deformations of compact Kähler surfaces II. Mathematische Zeitschrift, 258(3), 493-498. DOI Scopus15
  2006	Buchdahl, N. (2006). Algebraic deformations of compact Kahler surfaces. Mathematische Zeitschrift, 253(3), 453-459. DOI Scopus13
  2004	Buchdahl, N. (2004). Monads and bundles on rational surfaces. Rocky Mountain Journal of Mathematics, 34(2), 513-540. DOI Scopus12
  2003	Buchdahl, N. (2003). Compact Kähler surfaces with trivial canonical bundle. Annals of Global Analysis and Geometry, 23(2), 189-204. DOI Scopus2
  2000	Buchdahl, N. (2000). Blowups and gauge fields. Pacific Journal of Mathematics, 196(1), 69-111. DOI Scopus15
  2000	Buchdahl, N. (2000). A Nakai-Moishezon criterion for non-Kähler surfaces. Annales de L Institut Fourier, 50(5), 1533-1538. DOI Scopus19
  1999	Buchdahl, N., & Harris, A. (1999). Holomorphic connections and extension of complex vector bundles. Mathematische Nachrichten, 204(1), 29-39. DOI Scopus5
  1999	Buchdahl, N. (1999). Sequences of stable bundles over compact complex surfaces. Journal of Geometric Analysis, 9(3), 391-428. DOI Scopus5
  1999	Buchdahl, N. (1999). On compact Kähler surfaces. Annales de L'Institut Fourier, 49(1), 287-302. DOI Scopus89
  1999	Buchdahl, N. P. (1999). Sequences of stable bundles over compact complex surfaces. Journal of Geometric Analysis, 9(3), 426-427. Scopus5
  1995	Buchdahl, N. (1995). Review of Nagatomo, Y., Vanishing theorem for cohomology groups of c2-self-dual bundles on quaternionic Kähler manifolds. Mathematical Reviews, MR1319938.
  1993	Buchdahl, N. P. (1993). Instantons on nℂℙ<inf>2</inf>. Journal of Differential Geometry, 37(3), 669-687. DOI Scopus15
  1990	Buchdahl, N. P., Kwasik, S., & Schultz, R. (1990). One fixed point actions on low-dimensional spheres. Inventiones Mathematicae, 102(1), 633-662. DOI Scopus21
  1988	Buchdahl, N. P. (1988). Hermitian-Einstein connections and stable vector bundles over compact complex surfaces. Mathematische Annalen, 280(4), 625-648. DOI Scopus82
  1987	Buchdahl, N. P. (1987). Stable 2-bundles on Hirzebruch surfaces. Mathematische Zeitschrift, 194(1), 143-152. DOI Scopus29
  1986	Buchdahl, N. P. (1986). Instantons on CP<inf>2</inf>. Journal of Differential Geometry, 24(1), 19-52. DOI Scopus40
  1985	Buchdahl, N. P. (1985). Analysis on analytic spaces and non-self-dual yang-mills fields. Transactions of the American Mathematical Society, 288(2), 431-469. DOI Scopus14
  1983	Buchdahl, N. (1983). On the relattved e rham sequence. Proceedings of the American Mathematical Society, 87(2), 363-366. DOI Scopus28
  1977	Buchdahl, H. A., Buchdahl, N. P., & Stiles, P. J. (1977). On a relation between spherical and spheroidal harmonics. Journal of Physics A: General Physics, 10(11), 1833-1836. DOI Scopus13

• Theses

  Year	Citation
  2021	Fresacher, M. (2021). Approximation of Higher Degree Spectra Results for Twisted Laplace Operators.

I teach a variety of courses at all undergraduate and postgraduate levels, both in analysis and algebra.

• Current Higher Degree by Research Supervision (University of Adelaide)

  Date	Role	Research Topic	Program	Degree Type	Student Load	Student Name
  2023	Co-Supervisor	Topics in the Classification of Compact Complex Surfaces	Master of Philosophy	Master	Full Time	Mr Radee Stefanov Tchorbadjiev

• Past Higher Degree by Research Supervision (University of Adelaide)

  Date	Role	Research Topic	Program	Degree Type	Student Load	Student Name
  2020 - 2021	Co-Supervisor	Approximation of Higher Degree Spectra Results for Twisted Laplace Operators	Master of Philosophy	Master	Full Time	Mr Matthias Eduard Fresacher
  2018 - 2022	Co-Supervisor	Computer-based Assessments of High School Mathematics in Myanmar	Doctor of Philosophy	Doctorate	Full Time	Ms Hnin Nwe Nwe Tun
  2017 - 2021	Co-Supervisor	An investigation into factors affecting Grade 10 & 12 students' mathematics performance in Port Moresby, Papua New Guinea (PNG)	Doctor of Philosophy	Doctorate	Full Time	Mr Jerome Oko
  2014 - 2016	Co-Supervisor	Deformation Retractions from Spaces of Continuous Maps onto Spaces of Holomorphic Maps	Master of Philosophy	Master	Full Time	Mr Brett Simon Chenoweth
  2013 - 2016	Co-Supervisor	Holomorphic Flexibility Properties of Spaces of Elliptic Functions	Doctor of Philosophy	Doctorate	Full Time	Mr David James Bowman
  2012 - 2014	Co-Supervisor	Oka Theory of Riemann Surfaces	Master of Philosophy	Master	Full Time	William Crawford
  2010 - 2015	Principal Supervisor	Students' Experiences of Mathematics and How They Affect Further Engagement with Mathematics	Doctor of Philosophy	Doctorate	Full Time	Mr Patrick Waclaw Korbel
  2010 - 2013	Co-Supervisor	Holomorphic Flexibility Properties of Complements and Mapping Spaces	Doctor of Philosophy	Doctorate	Full Time	Mr Alexander Hanysz
  2009 - 2012	Principal Supervisor	Surface Shape Regions as Manifestations of a Socio-Economic Phenomenon a Solution to the Choropleth Mapping Problem	Master of Science in Mathematical and Computer Sciences	Master	Part Time	Dr John Massey
  2008 - 2011	Co-Supervisor	Acyclic Embeddings of Open Riemann Surfaces into Elliptic Manifolds	Doctor of Philosophy	Doctorate	Full Time	Mr Tyson Ritter
  2006 - 2008	Co-Supervisor	Invariant Bilinear Differential Pairings on Parabolic Geometrics	Doctor of Philosophy	Doctorate	Full Time	Mr Jens Kroeske
  2005 - 2008	Co-Supervisor	Regularized Equivariant Euler Classes and Gamma Functions	Doctor of Philosophy	Doctorate	Full Time	Mr Rongmin Lu
  2000 - 2003	Principal Supervisor	Yang-Mills connection to U(n)-bundles over compact Riemann surfaces	Master of Science in Mathematical and Computer Sciences	Master	Full Time	Mr Peter Lawrence

• Email: nicholas.buchdahl@adelaide.edu.au