Kyle Broder

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Postdoctoral Research Fellow ᐧ Mathematics ᐧ CV

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Priestley Building, 69-705

The University of Queensland, 

Brisbane, QLD, 4067

Email: k.broder@uq.edu.au

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I am interested in understand hyperbolic structures in various branches of mathematics and

science, and attempting to leverage relationships between them. My research has historically

been in the areas of complex analysis, differential geometry, and algebraic geometry. More

recently, I am exploring how hyperbolic complex geometry naturally emerges in calibrated geometries,

machine learning, statistics, and random matrix theory. 

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Conferences

• Analytic and Geometric Methods on Complex Manifolds [MATRIX]

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Publications and preprints 

• Holomorphic p-contact and s-symplectic line bundles (with Dan Popovici). 
  Preprint. [arXiv]. 

• Mortal solutions to the Kähler–Ricci flow (with Gang Tian). 
  To appear in the MATRIX Annals. [PDF] 

• Hyperbolicity and Schwarz Lemmas in Calibrated Geometries (with Anton Iliashenko & Jesse Madnick). 
  Preprint [arXiv]. 

• Vanishing Theorems for Hodge Numbers and the Calabi Curvature Operator (with Jan Nienhaus, Peter Petersen, James Stanfield, & Matthias Wink). 
  Preprint [arXiv]. 

• Remarks on Lang's Conjectural Characterisation of Hyperbolicity of Projective Manifolds (with Frédéric Campana). 
  Preprint [arXiv]. 

• Hermitian metrics with vanishing second Chern Ricci curvature (with Artem Pulemotov). 
  Bull. Lond. Math. Soc., 57, no. 1, 38–47, (2025). [Journal] [arXiv]. 

• A general Schwarz lemma for Hermitian manifolds (with James Stanfield). 
  Bull. Lond. Math. Soc., [Journal] [arXiv]. 

• Some remarks on the Wu–Yau theorem. 
  Preprint. [arXiv]. 

• (ε,𝛅)-Quasi-Negative Curvature and Positivity of the Canonical Bundle (with Kai Tang).
  J. Geom. Anal., 34, no. 180, 17 pp., (2024). [Journal] [arXiv]. 

• On the Gauduchon Curvature of Hermitian Manifolds (with James Stanfield).
  Int. J. Math., 34, no. 7, 2350039, (2023). [Journal] [arXiv]. 

• On the Nonnegativity of the Dirichlet Energy of a Weighted Graph.
  Bull. Aust. Math. Soc., 106, no. 2, pp. 301–305, (2022). [Journal]. 

• An Eigenvalue characterization of the dual EDM cone. 
  Bull. Aust. Math. Soc., 106, no. 1, pp. 67–69, (2022). [Journal]. 

• Remarks on the Quadratic Orthogonal Bisectional Curvature.
  J. Geom., 113, no. 2, Paper No. 39, 8 pp., (2022). [Journal] [arXiv].

• On Hermitian manifolds with vanishing curvature (with Kai Tang).
  Math. Z., 309, no. 12, 14 pp., (2024). [Journal] [arXiv]. 

• On the weighted orthogonal Ricci curvature (with Kai Tang).
  J. Geom. Phys., 193, no. 104783, 13 pp., (2023). [Journal] [arXiv].

• The Schwarz Lemma: An Odyssey.
  RMJ, 52, no. 4, pp. 1141–1155, (2022). [Journal] [arXiv]. 

• The Schwarz lemma in Kähler and non-Kähler geometry.
  Asian J. Math., 27, no. 1, pp. 121–134, (2023). [Journal] [arXiv]. 

• Second-order estimates for collapsed limits of Ricci-flat Kähler metrics.
  Can. Math. Bull., 66, no. 3, 912–926, (2023). [Journal] [arXiv]. 

• Twisted Kähler-Einstein Metrics and Collapsing. 
  Preprint. [arXiv]. 

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Other writing

• Complex manifolds of hyperbolic and non-hyperbolic type. 
  PhD thesis​. ANU. Supervised by Benjamin Andrews and Gang Tian. [PDF]

• On the theory of Stein Spaces. 
  Undergraduate thesis. ANU. Supervised by Alexander Isaev. [PDF]

• Lectures on Vector Calculus.
  Lecture notes for Applied Mathematics 1, MATH2305, ANU. [PDF]

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Fellowships and Grant Funding

• Marie Skłodowska-Curie fellowship. Curvature aspects of rigidity and flexibility of complex manifolds. 2024.

• Raybould visiting fellowship. Supporting research collaboration with Robert Bryant. 2026.

• IRL FAMSI funding. Supporting research collaboration with Hervé Gaussier. 2024. 2026.

Teaching

• MATH3402 - Functional Analysis. Semester 1, 2025. UQ.

• MATH4407 - Advanced Ordinary and Partial Differential Equations. Semester 2, 2024. UQ.

• MATH3402 - Differential Geometry. Semester 1, 2024. UQ. 

• MATH2305 - Applied Mathematics 1. Semester 1, 2022. ANU.

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Student supervision

• Henry Wood. Masters thesis, UQ. Cosupervised with Ramiro Lafuente. 2026–2027.

• Joseph Kwong. Masters thesis, UQ. Cosupervised with Ramiro Lafuente. 2025–2027.

• Aaron Tonkes. Undergraduate thesis, UQ. 2026.

• Thomas Hegarty. Research project, UQ. 2025–2026.

• David Alexander. Undergraduate thesis, UNSW. Cosupervised with Timothy Buttsworth. 2025–2026. 

• Xavier Sauvage. Undergraduate thesis, UQ. Cosupervised with Artem Pulemotov. 2024.
       Now doing a Masters thesis at Münster. 
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Last updated: February 8, 2026. 

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