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Research Interests

I am interested in classifying complex manifolds (in particular, projective manifolds) by means of the curvature of metrics that reside on them. I find Kobayashi hyperbolic manifolds (defined, for compact complex manifolds, by the non-existence of holomorphic maps from the complex line into them) particular fascinating. A folklore generalisation of a conjecture made by Kobayashi I find particularly enchanting: A compact Kobayashi hyperbolic manifold is projective and canonically polarised. Links to the existence of rational curves on Calabi--Yau manifolds and moduli theory are of notable interest. The 'elliptic counterparts' of hyperbolic manifolds, namely Oka manifolds and Special manifolds are tremendously exciting. 

A PDF version of my CV.

Education and Positions Held

September 2022 - Present

January 2019 - August 2022

January 2018 - December 2018

January 2015 - December 2017

Postdoctoral Research Fellowship. The University of Queensland. 

Funded by the Australian Research Council Discovery Project Grant held by Artem Pulemotov, Wolfgang Ziller, and Mark Gould

Ph.D. Australian National University and Beijing International Center for Mathematical Research.

Ph.D. thesis: Complex Manifolds of Hyperbolic and Non-Hyperbolic-Type.

Advised by Benjamin Andrews and Gang Tian.

B. Sc. Hon. Australian National University. 

Undergraduate thesis: On the Theory of Stein Spaces.

Advised by Alexander Isaev.

B. Sc. Australian National University.

Invited Talks

  • April 23, 2018 - Analytic functions of Several Complex Variables. The Australian National University.

  • October 29, 2019 - Canonical Metrics in Kähler geometry. The University of Sydney.

  • November 12, 2019 - Canonical Metrics in Kähler geometry. The Australian National University.

  • December 10, 2019 - Twisted Kähler--Einstein Metrics and Collapsing. Beijing International Center for Mathematical Research.

  • April 15, 2020 - Collapsed Limits of Ricci-flat Kähler metrics. Beijing International Center for Mathematical Research.

  • September 16, 2021 - The Schwarz Lemma: An Odyssey. The Australian National University.

  • December 7, 2021 - Recent developments on the curvature of Hermitian manifolds. AustMS, Geometry with Symmetries.

  • March 25, 2022 - A Kähler-Ricci flow proof of the Wu-Yau theorem (part 1). Australian Geometric PDE seminar.

  • April 1, 2022 - A Kähler-Ricci flow proof of the Wu-Yau theorem (part 2). Australian Geometric PDE seminar.

  • June 1, 2022 - Recent developments concerning the Bochner technique in the Hermitian category. Beijing International Center for Mathematical Research.

  • June 8, 2022 - Recent developments concerning the Bochner technique in the Hermitian category. Monash University.

  • November 1, 2022 - Curvature and Moduli -- Some intimations and propaganda. The University of Queensland.

  • November 25, 2022 - Curvature and Moduli -- Some intimations and propaganda. Australian Geometric PDE Seminar.

  • March 3, 2023 - Curvature Aspects of Hyperbolicity in Complex Geometry. Differential Geometry Days @ UQ. The University of Queensland.

  • May 17, 2023 - Complex Manifolds of Hyperbolic and Non-Hyperbolic-Type. The University of Adelaide.

  • May 18, 2023 - Curvature Aspects of Hyperbolicity in Complex Geometry. The University of Adelaide. 

  • June 3, 2023 - Recent Developmenst on the Schwarz Lemma; The University of Rome Tor Vergatta.

  • June 5, 2023 - Curvature Aspects of Hyperbolicity in Complex Geometry; Complex Analysis, Geometry, and Dynamics -- Portorož 2023.

  • October 16, 2023 - C^2 and C^3--estimates in Kähler geometry, The University of Queensland.

  • December 5, 2023 - A locality theorem for Einstein metrics on compact complex manifolds, The 67th annual meeting of the Australian Mathematical Society, Geometric Analysis Special Session.

  • December 8, 2023 - A locality theorem for Einstein metrics on compact complex manifolds, The 67th annual meeting of the Australian Mathematical Society, Topology Special Session.

Referee and Review Work

I have refereed for the following journals: Advances in Mathematics, the Journal of Geometry and Physics, and the Proceedings of the Edinburgh Mathematical Society.

I have written reviews for the following articles on ZbMath:

  • Fino, Anna; Grantcharov, Gueo; Vezzoni, Luigi; Solutions to the Hull-Strominger system with torus symmetry. Review linked here.

  • Foscolo, Lorenzo; Haskins, Mark; Nordström, Johannes; Complete noncompact G2-manifolds from asymptotically conical Calabi-Yau 3-folds. Review linked here.

  • Dajczer, M.; Onti, C.-R.; Vlachos, Th.; A class of Einstein submanifolds of Euclidean space. Review linked here.

  • Alonso, Izar; Salvatore, Francesca; On the existence of balanced metrics on six-manifolds of cohomogeneity one. Review linked here.

  • Mondello, Ilaria; Mondino, Andrea; Perales, Raquel; An upper bound on the revised first Betti number and a torus stability result for RCD spaces. Review linked here.

  • Anella, F.; Huybrechts, D.; Effectivity of semi-positive line bundles. Review linked here.

  • Belegradek, Igor; Index theory and deformations of open nonnegatively curved manifolds. Review linked here

Teaching

Semester 1, 2022

Semester 2, 2021

Semester 1, 2021

Semester 2, 2020

Semester 1, 2020

Semester 2, 2019

Semester 2, 2018

Semester 1, 2018

MATH1023. Multivariable Calculus and Modelling. The University of Sydney.

MATH1011. Applications of Calculus. The University of Sydney.
MATH1111. Introduction to Calculus. The University of Sydney.
MATH2021. Vector Calculus and Differential Equations. The University of Sydney.
PHAR1821. Pharmacy Practice 1. The University of Sydney.

MATH1023. Multivariable Calculus and Modelling. The University of Sydney.

MATH1021. Calculus of one variable. The University of Sydney.
MATH2021. Vector Calculus and Differential Equations. The University of Sydney.

MATH1014. Introduction to Linear Algebra. The University of Sydney.

MATH1014. Mathematics and Applications 2. Australian National University.

MATH1013. Mathematics and Applications 1. Australian National University.

MATH2305. Vector Calculus and Differential Equations. The Australian National University.

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