Research

My research lies at the interface of complex algebraic and differential geometry, gauge theory, and geometric analysis. I am particularly interested in Hermitian–Yang–Mills connections, moduli spaces, singularities, and degenerations of sheaves and bundles.

I am a member of the Geometry and Topology group at the University of Waterloo.

Papers and Preprints

• Point Singularities and Local Third Chern Classes for Rank-Two Torsion-Free Sheaves on Threefolds
  Preprint, 2026.
  arXiv
• Point Singularities and Bubbling in Degenerations of Rank-Two Bundles on Threefolds
  Preprint, 2026.
  arXiv
• Bubbling of rank two bundles over surfaces
  Preprint, 2025.
  arXiv
• Admissible Hermitian–Yang–Mills connections over normal varieties
  Math. Ann. (2025) arXiv
• On Vafa–Witten equations over Kähler manifolds
  J. Reine Angew. Math. (2024) arXiv
• Nonabelian Hodge correspondence for balanced Hermitian metrics of Hodge–Riemann type
  with Richard Wentworth.
  Math. Res. Lett. (2024) arXiv
• A Donaldson–Uhlenbeck–Yau theorem for normal varieties and semistable bundles on degenerating families
  with Richard Wentworth.
  Math. Ann. (2023) arXiv
• Compactness for Ω-Yang–Mills connections
  with Richard Wentworth.
  Calc. Var. Partial Differential Equations (2022) arXiv
• Reflexive sheaves, Hermitian–Yang–Mills connections, and tangent cones
  with Song Sun.
  Invent. Math. (2021) arXiv
• Analytic tangent cones of admissible Hermitian–Yang–Mills connections
  with Song Sun.
  Geometry & Topology (2021) arXiv
• Singularities of Hermitian–Yang–Mills connections and the Harder–Narasimhan–Seshadri filtration
  with Song Sun.
  Duke Math. J. (2020) arXiv
• Algebraic tangent cones of reflexive sheaves
  with Song Sun.
  Int. Math. Res. Not. (2018) arXiv

Teaching

Fall 2026

PMATH 450: Measure Theory
MWF 2:30–3:20 pm, E2 1736
Office hours: Thursday 1:00–2:00 pm, MC 5324

Seminars and Events

Seminars

• University of Waterloo Geometry and Topology Seminar
• University of Waterloo Differential Geometry Working Seminar
• Fields Institute Geometric Analysis Colloquium

Upcoming Talks and Events

• Weeklong Lecture Series, University of Wisconsin–Madison, October 12–17, 2026.
• Co-organizer, New Developments in Analytic and Geometric Aspects of Gauge Theory, IASM-BIRS Workshop, Hangzhou, China, May 30–June 4, 2027.