Shih-Kai Chiu

Shih-Kai Chiu photo

Visiting Assistant Professor

University of California, Irvine

Department of Mathematics

340 Rowland Hall

Irvine, CA 92697-3875

Office: 410P

Email: shihkaic@uci.edu

Brief Bio

Since Winter 2025, I have been a Visiting Assistant Professor at University of California, Irvine, where my mentor is Xiangwen Zhang. During Fall 2024, I was a Postdoc at the SLMath (formerly MSRI) under the program Special Geometric Structures and Analysis, where my mentor was Mark Haskins.

In the academic year 2023–2024, I was a Postdoctoral Scholar at Vanderbilt University, mentored by Ioana Suvaina. From 2021 to 2023, I was a Postdoctoral Research Associate in Special Holonomy at the University of Oxford, where my mentor was Jason D. Lotay.

I received my PhD in Mathematics in August 2021 from the University of Notre Dame, under the supervision of Gábor Székelyhidi. I am interested in geometric analysis and complex differential geometry, as well as related areas.


Research

My research interests lie in Kähler geometry, manifolds with special holonomy, and calibrated geometry, with a particular focus on Calabi–Yau manifolds and special Lagrangian submanifolds.

Calabi–Yau manifolds play a central role in both mathematics and physics. Many important phenomena were first observed in this setting before generalizing more broadly. I have worked on existence and classification results for singular Kähler–Einstein metrics and Calabi-Yau metrics with maximal volume growth.

Special Lagrangian submanifolds are half-dimensional, volume-minimizing Lagrangian submanifolds in Calabi–Yau manifolds. In string theory, they arise as boundary conditions for open strings, and counting them is expected to yield invariants of the ambient Calabi–Yau manifold. These special submanifolds are difficult to construct in the compact setting. I have recently constructed new examples in certain compact Calabi–Yau 3-folds.

In certain extreme situations, the geometry of compact Calabi-Yau manifolds can be understood through singular Kähler–Einstein metrics and Calabi–Yau metrics with maximal volume growth. This perspective informs the study of special Lagrangian geometry, and my two research directions merge in this interplay. A long-term goal, however, is to understand Calabi–Yau manifolds and special Lagrangian submanifolds in generic regions of their moduli spaces.

More recently, I have also become interested in G2 geometry and gauge theory.

Papers & preprints


Teaching

At Irvine: At Vanderbilt: At Notre Dame:

Activities organized


Invited Talks

Conferences and workshops

Seminars