Dr

Kyle Broder

Email: 

Background

I am interested in leveraging curvature in differential geometry to understand problems in topology, algebraic geometry, and complex analysis. More specifically, I'm interested in:

  • Curvature aspects of Kaehler geometry, Hermitian geometry and Finsler geometry. In particular, the existence of Einstein metrics or metrics with distinguished curvature properties.

  • Kobayashi hyperbolic manifolds, and more generally, the algebro-geometric properties of complex manifolds such as the positivity of the canonical bundle, distribution of rational and entire curves.

  • ​The Bochner technique, most notably the Schwarz lemma.

  • Calibrated geometry.

Availability

Dr Kyle Broder is:
Available for supervision

Qualifications

  • Doctor of Philosophy of Mathematics, Australian National University

Research interests

  • Complex differential geometry

  • Calibrated geometry

  • G-structures

  • Einstein metrics

  • The Bochner technique

Search Professor Kyle Broder’s works on UQ eSpace

12 works between 2022 and 2026
All (12) Journal Article (12)

1 - 12 of 12 works

2026

Journal Article

Holomorphic <i>p</i>-Contact and <i>s</i>-Symplectic Line Bundles

Broder, Kyle and Popovici, Dan (2026). Holomorphic p-Contact and s-Symplectic Line Bundles. Journal of Geometric Analysis, 36 (4) 137. doi: 10.1007/s12220-026-02380-6

Holomorphic <i>p</i>-Contact and <i>s</i>-Symplectic Line Bundles

2026

Journal Article

A general Schwarz lemma for Hermitian manifolds

Broder, Kyle and Stanfield, James (2026). A general Schwarz lemma for Hermitian manifolds. Bulletin of the London Mathematical Society, 58 (1) e70269, 1-13. doi: 10.1112/blms.70269

A general Schwarz lemma for Hermitian manifolds

2025

Journal Article

On Hermitian manifolds with vanishing curvature

Broder, Kyle and Tang, Kai (2025). On Hermitian manifolds with vanishing curvature. Mathematische Zeitschrift, 309 (1) 12, 1-14. doi: 10.1007/s00209-024-03651-0

On Hermitian manifolds with vanishing curvature

2024

Journal Article

(ε,δ)–Quasi-negative curvature and positivity of the canonical bundle

Broder, Kyle and Tang, Kai (2024). (ε,δ)–Quasi-negative curvature and positivity of the canonical bundle. Journal of Geometric Analysis, 34 (6) 180. doi: 10.1007/s12220-024-01619-4

(ε,δ)–Quasi-negative curvature and positivity of the canonical bundle

2024

Journal Article

Hermitian metrics with vanishing second Chern Ricci curvature

Broder, Kyle and Pulemotov, Artem (2024). Hermitian metrics with vanishing second Chern Ricci curvature. Bulletin of the London Mathematical Society, 57 (1), 38-47. doi: 10.1112/blms.13179

Hermitian metrics with vanishing second Chern Ricci curvature

2023

Journal Article

On the weighted orthogonal Ricci curvature

Broder, Kyle and Tang, Kai (2023). On the weighted orthogonal Ricci curvature. Journal of Geometry and Physics, 193 104783, 104783-193. doi: 10.1016/j.geomphys.2023.104783

On the weighted orthogonal Ricci curvature

2023

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

On the Gauduchon curvature of Hermitian manifolds

2023

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

Second-Order Estimates for Collapsed Limits of Ricci-flat Kähler Metrics

2023

Journal Article

The Schwarz lemma in Kähler and non-Kähler geometry

Broder, Kyle (2023). The Schwarz lemma in Kähler and non-Kähler geometry. Asian Journal of Mathematics, 27 (1), 121-134. doi: 10.4310/AJM.2023.v27.n1.a5

The Schwarz lemma in Kähler and non-Kähler geometry

2022

Journal Article

An eigenvalue characterisation of the dual edm cone

Broder, Kyle (2022). An eigenvalue characterisation of the dual edm cone. Bulletin of the Australian Mathematical Society, 106 (1), 67-69. doi: 10.1017/S0004972721000915

An eigenvalue characterisation of the dual edm cone

2022

Journal Article

Remarks on the quadratic orthogonal bisectional curvature

Broder, Kyle (2022). Remarks on the quadratic orthogonal bisectional curvature. Journal of Geometry, 113 (2) 39, 2. doi: 10.1007/s00022-022-00653-3

Remarks on the quadratic orthogonal bisectional curvature

2022

Journal Article

THE SCHWARZ LEMMA: AN ODYSSEY

Broder, Kyle (2022). THE SCHWARZ LEMMA: AN ODYSSEY. Rocky Mountain Journal of Mathematics, 52 (4), 1141-1155. doi: 10.1216/rmj.2022.52.1141

THE SCHWARZ LEMMA: AN ODYSSEY

Availability

Dr Kyle Broder is:
Available for supervision

Looking for a supervisor? Read our advice on how to choose a supervisor.

Available projects

  • 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.

Supervision history

Current supervision

Enquiries

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