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
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
- Oberseminar Differentialgeometrie, Münster, 07/2020 (Online)
- Geometric Analysis Seminar, CUNY, 06/2020 (Online, see seminar page for video)
- Differential Geometry Seminar, NCTS, Taipei, 06/2019
- Geometric Analysis Seminar, Notre Dame, 04/2019
Teaching
- MATH 10550, Fall 2019, Instructor
- MATH 10350, Fall 2018, Teaching Assistant
- MATH 20580, Spring 2018, Teaching Assistant
- MATH 10550, Fall 2017, Teaching Assistant