I am a differential geometer and professor of mathematics at Duke University. For the last 10+ years my research focus has been on the Hodge theory, specifically complex geometric properties of period maps. Before that, I worked on projects in Finsler geometry, calibrated geometry, and the geometry and topology of rational homogeneous varieties. I have a side interest in formalization of mathematics and the proof assistant Lean.
PhD Students
Daniel Zhou, co-advising with Fan Wei thesis work on formalization and combinatorics.
Chongyao Chen: Hodge theory of Calabi--Yau varieties, Duke 2025 (co-advised with Kirsten Wickelgren).
Panchali Nag: Differential Geometry Tools for Data Analysis, Duke 2021 (co-advised with Ingrid Daubechies).
Curtis Porter: The Local Equivalence Problem for 7-dimensional, 2-nondegenerate CR Manifolds whose Cubic Form is of Conformal Unitary Type , Texas A&M 2016 (co-advised with J.M. Landsberg & Igor Zelenko).
Undergraduate Students
Xiayimei Han, Hodge representations of Calabi-Yau 3-folds, Duke 2020.
Undergraduate Research Projects
Computational Algebraic Number Theory with Geometric Applications, with Farid Hosseinijafari, summer 2026.
Formalization of Mathematics, summer 2025.
Formalization of Mathematics, summer 2024.
Automated Theorem Proving and Proof Verification, summer 2023.
Service
Department Liaison. Dedicated, neutral conduit through which comments and concerns about departmental culture, atmosphere and behavior can be communicated to department officers and/or deans; and a discreet resource and sounding board for any department member.
Member, Provost's Academic Programs Committee.
Assistant Director, Duke Rhodes iiD.
Member, AMS Committee on Science Policy.
Editor, Annals of Formalized Mathematics.
Organizing
Organizer, iiD Colloquium on Formalization of Mathematics. Speakers: Alex Kontorovich (Fall 2026), Emily Rhiel (Spring 2026), Kaiyu Yang (Fall 2025), Matthew Ballard (Spring 2025).
Co-organizer, Program on Hodge Theory at the Simons-Laufer Matematical Sciences Institute, Fall 2029, with Ben Bakker, Laure Flapan, Robert Friedman, Radu Laza, Christian Schnell, Junliang Shen, Qizheng Yin.