Lachlan MacDonald

Lachlan MacDonald

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences

I completed my PhD at the University of Wollongong under the supervision of A. Rennie. The title of my thesis is ``Characteristic Classes of Foliated Manifolds in Noncommutative Geometry", wherein I studied how formulae for characteristic classes (such as the Godbillon-Vey invariant) could be obtained using equivariant KK-theory and local index formulae.

My current research is into the equivariant cohomology of foliated manifolds, with a view to defining characteristic classes for singular foliations. In my spare time I daydream about applications of differential-geometric ideas to learning theory, physics and economics.

  • Journals

    Year Citation
    2020 MacDonald, L. (2020). Equivariant KK-theory for non-Hausdorff groupoids. Journal of Geometry and Physics, 154, 17 pages.
    2016 Pan, A. V., MacDonald, L., Baiej, H., & Cooper, P. (2016). Theoretical consideration of superconducting coils for compact superconducting magnetic energy storage systems. IEEE Transactions on Applied Superconductivity, 26(3), 1-5.
    DOI WoS7
    MacDonald, L., & Rennie, A. (n.d.). The Godbillon-Vey invariant in equivariant $KK$-theory. Th., 5, 249-294.
    MacDonald, L. E. (n.d.). Hierarchies of holonomy groupoids for foliated bundles.
    MacDonald, L. E. (n.d.). The holonomy groupoids of singularly foliated bundles.
    Macdonald, L., Mathai, V., & Saratchandran, H. (n.d.). On the Chern character in Higher Twisted K-theory and spherical
  • Internet Publications

    Year Citation
    MacDonald, L. (n.d.). A characteristic map for the holonomy groupoid of a foliation.

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