
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
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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
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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. |