About

Professor Yu-Shen Lin is an Associate Professor in the Department of Mathematics & Statistics at Boston University. He is a member of the Geometry and Physics research group. For more information about Professor Lin, please see his personal webpage.

Research topics

• Pure mathematics
• Mathematics
• Computer Science
• Mathematical analysis
• Geometry
• Physics

Selected publications

• A convergence result for mean curvature flow of totally real submanifolds

  Mathematische Zeitschrift · 2026-02-28

  articleOpen accessSenior author

  Abstract We establish a convergence result for the mean curvature flow starting from a totally real submanifold which is “almost minimal" in a precise, quantitative sense. This extends, and makes effective, a result of Li (Math Z 271(1–2): 313–342, 2012 ) for the Lagrangian mean curvature flow.

  PublisherOA PDFDOI

• The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces

  Journal of Differential Geometry · 2025-12-29

  articleSenior author
  PublisherDOI

• Scattering diagrams from holomorphic discs in log Calabi-Yau surfaces

  Journal of Differential Geometry · 2025-05-01

  articleSenior author
  PublisherDOI

• SYZ mirror symmetry for del Pezzo surfaces and affine structures

  Advances in Mathematics · 2024-01-18 · 3 citations

  articleSenior author
  PublisherDOI

• A convergence result for Mean Curvature Flow of totally real submanifolds

  arXiv (Cornell University) · 2024-05-17

  preprintOpen accessSenior author

  We establish a convergence result for the mean curvature flow starting from a totally real submanifold which is "almost minimal" in a precise, quantitative sense. This extends, and makes effective, a result of H. Li for the Lagrangian mean curvature flow.

  PublisherOA PDFDOI

• Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds

  arXiv (Cornell University) · 2024-10-23

  preprintOpen accessSenior author

  We construct special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds fibered by K3 surfaces. As these 3-folds collapse, the special Lagrangians shrink to 1-dimensional graphs in the base, mirroring the conjectured tropicalization of holomorphic curves in collapsing SYZ torus-fibered Calabi-Yau manifolds. This confirms predictions of Donaldson and Donaldson-Scaduto in the Calabi-Yau setting. Additionally, we discuss our results in the contexts of the Thomas-Yau conjecture, the Donaldson-Scaduto conjecture, and mirror symmetry.

  PublisherOA PDFDOI

• Collapsing of $ALH^*$-gravitational instantons

  Communications in Analysis and Geometry · 2023-01-01

  preprintOpen access1st authorCorresponding

  We showed that a sequence of ALH*-gravitational instantons from pairs consisting of a weak del Pezzo surface and a smooth anti-canonical divisor towards a large complex structure limit introduced by Collins, Jacobs and the first author collapsing to a punctured plane with a special Kahler metric, which can be viewed as a non-compact version of the collapsing result of Gross-Wilson. We provide a partial compactification of the moduli space of pointed ALH*-gravitational instantons with respect to the pointed Gromov-Hausdorff topology and locally is a polyhedron complex.

  PublisherOA PDFDOI

• Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces

  Surveys in Differential Geometry · 2023-01-01

  articleSenior author
  PublisherDOI

• SYZ mirror symmetry for del Pezzo surfaces and affine structures

  arXiv (Cornell University) · 2022-06-03 · 1 citations

  preprintOpen accessSenior author

  We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperKähler rotation toward the large complex structure limit point. As a corollary, we compute the limit of the complex affine structure of the special Lagrangian fibrations constructed by Collins--Jacob--Lin in $\mathbf{P}^1\times \mathbf{P}^1$ arXiv:1904.08363 and compare it with the integral affine structures used in the work of Carl--Pumperla--Siebert arXiv:2205.07753. We also construct the Floer-theoretical Landau--Ginzburg mirrors of smoothing of $A_n$-singularities and monotone del Pezzo surfaces, by using the gluing method of Cho--Hong--Lau arXiv:1810.02045 and Hong--Kim--Lau arXiv:1805.11738. They agree with the result of hyperKähler rotation.

  PublisherOA PDFDOI

• Period domains for gravitational instantons

  Transactions of the American Mathematical Society · 2022-11-16

  articleSenior author

  Based on the uniformization theorems of gravitation instantons by Chen–Chen [Acta Math. 227 (2021), pp. 263–307], Chen–Viaclovsky [<italic>Gravitational instantons with quadratic volume growth</italic>, 2021], Collins–Jacob–Lin [Forum Math. Sigma (2021)], and Hein–Sun–Viaclovsky–Zhang [<italic>Gravitational instantons and del Pezzo surfaces</italic>], we prove that the period maps for the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal upper L normal upper H Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">\mathrm {ALH}^{\ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal upper L normal upper G"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {ALG}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal upper L normal upper G Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">G</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">\mathrm {ALG}^{\ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.

  PublisherDOI

Recent grants

• Gravitational Instantons, Mirror Symmetry, and Enumerative Geometry

  NSF · $158k · 2022–2025

Frequent coauthors

• Tsung-Ju Lee

  8 shared

• Tristan C. Collins

  7 shared

• Adam Jacob

  6 shared

• Siu-Cheong Lau

  Boston University

  5 shared

• Man-Wai Cheung

  The University of Tokyo

  3 shared

• Er-Shuo Zhuang

  National Sun Yat-sen University

  2 shared

• Jingyu Zhao

  Harvard University Press

  2 shared

• Y. Y. Lin

  National Tsing Hua University

  2 shared