Kyle Broder

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Postdoctoral Research Fellow ᐧ Mathematics

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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 a complex geometer working at the interface of algebraic geometry, complex analysis,

and differential geometry. My research program centres around Kobayashi hyperbolicity, a

class of complex manifolds with deep connections to several branches of mathematics,

ranging from Einstein metrics to Diophantine geometry. 

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Conferences

• Analytic and Geometric Methods on Complex Manifolds [MATRIX] [Mug shot]

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Publications and preprints 

• Holomorphic p-contact and s-symplectic line bundles (with Dan Popovici). 
  Journal of Geometric Analysis (special issue "Proc. Conf. Complex Analysis, Geometry, and Dynamics III - Portorož 2024", dedicated to Josip Globevnik for his 80th birthday). [Journal] [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]. 

• Weakly Special Manifolds with no Rational Curves (with Frédéric Campana). 
  To appear in the Bulletin de la Société Mathématique de France.  [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 Ben 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]

• Lauret's question on Gauduchon Ricci-flat metrics. [PDF]

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Fellowships and Grant Funding

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

• CNRS funding. Supporting research collaboration with Hervé Gaussier. 2024.

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

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

Teaching

• Functional Analysis (UQ, MATH3402), Sem1, 2025. 

• Advanced Ordinary and Partial Differential Equations (UQ, MATH4407), Sem2, 2024. 

• Differential Geometry (UQ, MATH3402), Sem1, 2024.  

• Applied Mathematics 1 (ANU, MATH2305) Sem1, 2022. 

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Student supervision

• Henry Wood. Masters thesis, UQ. Co-supervised with Ramiro Lafuente. 2026–2027.

• Joseph Kwong. Masters thesis, UQ. Co-supervised with Ramiro Lafuente. 2025–2027.

• Aaron Tonkes. Undergraduate thesis, UQ. 2026.

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

• David Alexander. Undergraduate thesis, UNSW. Co-supervised with Timothy Buttsworth. 2025–2026. 

• Xavier Sauvage. Undergraduate thesis, UQ. Co-supervised with Artem Pulemotov. 2024.
       Now doing a Masters thesis at Münster. 
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Last updated: April 12, 2026. 

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