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Department of Mathematics, Columbia University
2990 Broadway, New York, NY 10027, USA
Email: xss at math dot columbia dot edu
Office: 415
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I am a Ritt Assistant Professor at Columbia University.
Previously, I completed my PhD in Mathematics at Northwestern University in Spring 2021 under the guidance of Ben Weinkove.
My research interests are in complex geometry and partial differential equations, specifically, on complex geometric flows and constant scalar curvature problems.
Curriculum Vitae (updated July 2023)
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| Teaching
Fall 2023: Analysis and Optimization (MATHUN 2500)
Winter 2023: Calculus 3 (MATHUN 1201)
Fall 2022: Analysis and Optimization (MATHUN 2500)
Winter 2022: Calculus 1 (MATHUN 1101)
Fall 2021: Calculus 1 (MATHUN 1101)
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| Publications
- (with Pranay Talla) Non-preservation of α-concavity for the porous medium equation in higher dimensions, arxiv.2403.13226.
- (with Shuang Liang and Kevin Smith) The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature and Oeljeklaus-Toma manifolds,
Bulletin of the London Mathematical Society, Vol 56, no 3 (2024), arxiv.2307.03665.
- (with Kevin Smith) The continuity equation on Hopf and Inoue surfaces,
International Mathematics Research Notices (2023), arxiv.2209.05473.
- (with Mehdi Lejmi) Canonical almost Kähler metrics dual to general plane-fronted Lorentzian metrics,
Mathematische Zeitschrift, Vol 303, no 4 (2023), arxiv.2208.00026.
- A Chern-Calabi flow on Hermitian manifolds,
The Journal of Geometric Analysis, Vol 32, no 4 (2022), arxiv.2011.09683.
- The Kähler-Ricci flow, holomorphic vector fields and Fano bundles,
Transactions of the AMS, Vol 374, no 9 (2021), arxiv.2004.00042.
- Estimates for metrics of constant Chern scalar curvature,
Mathematical Research Letters, Vol 28, no 5 (2021), arxiv.1909.13445.
- (with A. Williams) A k-ary middle levels conjecture,
Proceedings of the 23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games (2021).
- (with A. Williams) A middle levels conjecture for multiset permutations with uniform frequency, Williams College Technical Report CSTR-201901.
- (with P. Guan) A rigidity theorem for hypersurfaces in space form,
Contemporary Mathematics, AMS, Vol 644 (2015), pp 61-65, arxiv.1306.1581.
- (with A. Williams) A 'Hot Potato' Gray code for permutations,
Electronic Notes in Discrete Mathematics Vol 44 (2013), pp 89-94.
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