Postdoctoral Research Fellow
Overview
Research Interests
- Kobayashi hyperbolicity
- Oka manifolds
- Rationally connected manifolds
- Kähler--Einstein metrics
- Curvature characterisations of notions in algebraic and complex-analytic geometry
Qualifications
- Doctor of Philosophy of Mathematics, Australian National University
Publications
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Journal Article: On the Gauduchon curvature of Hermitian manifolds
Broder, Kyle and Stanfield, James (2023). On the Gauduchon curvature of Hermitian manifolds. International Journal of Mathematics, 34 (07) 2350039. doi: 10.1142/s0129167x23500398
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Journal Article: Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics
Broder, Kyle (2023). Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics. Canadian Mathematical Bulletin, 66 (3), 1-15. doi: 10.4153/S0008439522000765
Available Projects
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Complex Differential Geometry
The study of complex manifolds via methods of differential geometry. This topic has strong links to a number of fields, ranging from algebraic geometry and number theory, to complex analysis, group theory, and homotopy theory.
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Invariant metrics in complex analysis
One of the most important classes of compact complex manifolds are those for which every holomorphic map from the complex plane into them is constant. These manifolds can be described by the existence of a non-degenerate distance function that is invariant under the automorphism group.
Publications
Journal Article
-
On the Gauduchon curvature of Hermitian manifolds
Broder, Kyle and Stanfield, James (2023). On the Gauduchon curvature of Hermitian manifolds. International Journal of Mathematics, 34 (07) 2350039. doi: 10.1142/s0129167x23500398
-
Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics
Broder, Kyle (2023). Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics. Canadian Mathematical Bulletin, 66 (3), 1-15. doi: 10.4153/S0008439522000765
Possible Research Projects
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
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Complex Differential Geometry
The study of complex manifolds via methods of differential geometry. This topic has strong links to a number of fields, ranging from algebraic geometry and number theory, to complex analysis, group theory, and homotopy theory.
-
Invariant metrics in complex analysis
One of the most important classes of compact complex manifolds are those for which every holomorphic map from the complex plane into them is constant. These manifolds can be described by the existence of a non-degenerate distance function that is invariant under the automorphism group.
