Shih-Kai Chiu

My name is Shih-Kai Chiu (邱詩凱). I am a fifth year math graduate student at the University of Notre Dame, studying under the supervision of Gábor Székelyhidi. I am interested in geometric analysis and complex geometry, as well as related areas. Before coming to Notre Dame, I studied for my M.S. in math and B.S. in chemical engineering at National Taiwan University.

Write me an email.

Student Seminar Fall 2020

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Research

I am currently interested in complete Calabi-Yau manifolds with maximum volume growth. Special examples include AC Calabi-Yau manifolds (Tian-Yau, Conlon-Hein). I am studying their constructions (Li, Conlon-Rochon, Székelyhidi) as well as deformations/uniqueness problems (Conlon-Hein, Székelyhidi). A parallel subject is the asymptotic metric behavior of isolated conical singularities (Hein-Sun).

Papers & preprints

• Subquadratic harmonic functions on Calabi-Yau manifolds with Euclidean volume growth, arXiv:1905.12965 (2019), submitted. ±
  ABSTRACT. We prove that on a complete Calabi-Yau manifold \(M\) with Euclidean volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville type theorem for harmonic \(1\)-forms, which follows from a new local \(L^2\) estimate of the differential. We also give another proof based on the construction of harmonic functions with polynomial growth in Ding, and the algebraicity of tangent cones in Liu-Székelyhidi.

Seminar Talks

• Geometric Analysis Seminar, Notre Dame, 11/2020
• Oberseminar Differentialgeometrie, Münster, 07/2020
• Geometric Analysis Seminar, CUNY, 06/2020 (See seminar page for video)
• Differential Geometry Seminar, NCTS, Taipei, 06/2019
• Geometric Analysis Seminar, Notre Dame, 04/2019

Teaching

• MATH 10560, Spring 2021, Teaching Assistant
• MATH 10550, Fall 2019, Instructor
• MATH 10350, Fall 2018, Teaching Assistant
• MATH 20580, Spring 2018, Teaching Assistant
• MATH 10550, Fall 2017, Teaching Assistant