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Faculty of Mathematics

 

I am a Royal Society University Research Fellow at Cambridge University. I am looking for a Ph.D student starting in Oct 2025.

 

 

Research Interest: Calabi-Yau metrics, special Lagrangians, special holonomy, gauge theory

 

 

Publications and preprints:

Calabi-Yau metrics and SYZ conjecture: 

• A new complete Calabi-Yau metric on C3 , Inventiones mathematicae, July 2019, Volume 217, Issue 1, pp 1-34. 

• A gluing construction of collapsing Calabi-Yau metrics on K3 fibred 3-folds, Geometric and Functional Analysis, August 2019, Volume 29, Issue 4, pp 1002-1047.

• On collapsing Calabi-Yau fibrations, J. Differential Geom. 117(3): 451-483 (March 2021). 

• Diameter bounds for degenerating Calabi-Yau metrics, joint with Valentino Tosatti, J. Differential Geom. 127 (2024), no. 2, 603--614. 

• On the collapsing of Calabi-Yau manifolds and Kaehler-Ricci flows, joint with Valentino Tosatti. J. Reine Angew. Math. 800 (2023), 155--192.

• Collapsing Calabi-Yau fibrations and uniform diameter bounds, Geom. Topol. 27 (2023), no. 1, 397--415. 

• Complete Calabi-Yau metrics in the complement of two divisors, joint with Tristan Collins, arXiv:2203.10656. 

•Special Kahler geometry and holomorphic Lagrangian fibrations, joint with Valentino Tosatti, C. R. Math. Acad. Sci. Paris 362 (2024), Special issue, 171--196. 

 

• SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family, Acta Math. 229 (2022), no. 1, 1–53. 

• SYZ geometry for Calabi-Yau 3-folds: Taub-NUT and Ooguri-Vafa type metrics. Mem. Amer. Math. Soc. 292 (2023), no. 1453, v+126 pp. ISBN: 978-1-4704-6782-1; 978-1-4704-7698-4

• Uniform Skoda integrability and Calabi-Yau degeneration, Anal. PDE17 (2024), no. 7, 2247--2256. 

• Metric SYZ conjecture and non-archimedean geometry, Duke Math. J.172 (2023), no. 17, 3227--3255.

• Survey on the metric SYZ conjecture and non-archimedean geometry, Internat. J. Modern Phys. A 37 (2022), no. 17, Paper No. 2230009, 44 pp.

• Metric SYZ conjecture for certain toric Fano hypersurfaces, Camb. J. Math. 12 (2024), no. 1, 223--252.  

• Intermediate complex structure limit for Calabi-Yau metrics, arXiv:2305.02258

 

Special Lagrangians and Thomas-Yau conjecture:

• Thomas-Yau conjecture and holomorphic curves, arXiv:2203.01467, accepted by EMS survey

• Quantitative Thomas-Yau uniqueness, arXiv:2207.08047. 

• Uniqueness of some cylindrical tangent cones to special Lagrangians, Geom. Funct. Anal. 33 (2023), no. 2, 376--420.

• Special Lagrangian pair of pants, arxiv: 2310.15443

• On the Donaldson-Scaduto conjecture, joint with Saman Esfahani, https://arxiv.org/abs/2401.15432

Gauge theory (Nahm transform and analytic aspects):

• Local Nahm transform and singularity formation of ASD connections, Communications in Mathematical Physics, pp 1-38. 

• Mukai duality on K3 surfaces from the differential geometric perspective, arXiv:1908.05017. 

• Mukai duality on adiabatic coassociative fibrations, arXiv:1908.08268, accepted by PAMQ

• Bubbling phenomenon for Hermitian Yang-Mills connections, International Mathematics Research Notices, Volume 2021, Issue 6, March 2021, Pages 46574678. 

• A note on singular Hermitian Yang-Mills connections,  Math. Res. Lett.30 (2023), no. 1, 167--184.

•Fueter sections and $Z_2$-harmonic 1-forms, joint with Saman Esfahani, https://arxiv.org/abs/2410.06367

 

G2 metrics (special holonomy):

• Dirichlet problem for maximal graphs of higher codimension, Int. Math. Res. Not. IMRN 2022, no. 3, 2159–2179.

• Iterated collapsing phenomenon on G2-manifolds, Pure Appl. Math. Q. 18 (2022), no. 3, 971–1036.

 

 

 

Research Groups

Algebraic Geometry
Differential Geometry & Topology

Room

E0.04