Research Interests: 

My research area is algebraic geometry, with a particular focus on the derived category of coherent sheaves. My works explore several interconnected topics. Along one direction, I study Bridgeland stability condition, which is a stability condition defined on the derived category of coherent sheaves on an algebraic variety. Our recent work contributes to the understanding of Bridgeland stable objects. In many cases, the stable objects form a well-behaved topological space called the moduli space. By performing intersection theory on this moduli space, one can derive enumerative invariants of the variety, such as the famous result that a cubic surface contains exactly 27 lines. My other research direction focuses on a "categorified" enumerative theory–motivic Donaldson-Thomas theory. This theory produces categorification of enumerative invariants of stable sheaves on smooth Calabi-Yau 3-folds.

Publications and Preprints: 

• Bridgeland/weak Stability Conditions under Spherical Twist Associated to a Torsion Sheaf. (with Tristan Collins, Jason Lo, Shing-Tung Yau) ,  arXiv 2411.18554 

• Moduli of sheaves on fourfolds as derived Lagrangian intersections, (with Nachiketa Adhikari), arXiv:2403.00727, under the first round revision of Nagoya Math. J..

• Stability for line bundles and deformed Hermitian-Yang-Mills Equation on some elliptic surfaces. (with Tristan Collins, Jason Lo, Shing-Tung Yau) arXiv:2306.05620, submitted.

• Weak stability conditions as limits of Bridgeland stability conditions, (with TristanCollins, Jason Lo, Shing-Tung Yau) arXiv:2410.02466, accepted by Can. J. Math.

• D-critical locus structure on the Hilbert schemes of some local toric Calabi-Yau threefolds. (with Sheldon Katz) Math Res Lett, accepted, arXiv:2009.05529 

• D-critical loci for length n sheaves on local toric Calabi-Yau 3-folds. (with Sheldon Katz) Bull. Lond. Math. Soc., 54(6) 2101-2116, 2022, arXiv:2108.13510

• Orientation data for coherent sheaves on local P2. Math. Res. Lett., to appear arXiv:1809.01776

In preparation: 

• Stability of the Cotangent Bundle on Some Surfaces. (with Tristan Collins, Jason Lo, Shing-Tung Yau), draft available upon request.

Other writings:

• Motivic Donaldson-Thomas invariant: construction and computation, ICCM proceedings 2020.

• Stability and the deformed Hermitian-Yang-Mills equation. (with Tristan Collins) Surveys in Differential Geometry. 24 (2019), 1-38. arXiv:2004.04831  

• Symmetry is the sine qua non of shape. Li, Y., Sawada, T., Shi, Y., Steinman, R.M., Pizlo, Z. Book Chapter in Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. 2013

• A Bayesian model of binocular perception of 3D mirror symmetrical polyhedra. Li, Y., Sawada, T., Shi, Y., Kwon, T.,  Pizlo, Z. Journal of Vision, 11(4):11, 1-20, 2011

Invited Talks:

• AWM Research Symposium, Madison, WI, May 2025

• Geometry and Physics Seminar, Boston University, Feb 2025

• Algebraic Geometry Seminar, University of Maryland, May 2024

• GPRT seminar, Northeastern University, Feb 2024

• CATS 7 conference, CIRM, France, Oct 2023

• AWM Research Symposium, Atlanta, GA, Sep 2023

• Brazil-China Joint Mathematical Meeting, Foz do Iguaçu, Brazil, Jul 2023

• Algebraic Geometry seminar, Boston College, Feb 2023

• AMS sectional meeting, University of Utah, Oct 2022

• Algebraic Geometry seminar, Duke University, July 2022

• Enumerative Geometry seminar, USCD, Jun 2022 (online)

• Geometry and Analysis seminar, Oxford, Jan 2022 (online)

• ICCM, University of Science and Technology of China, Dec 2020 (online)

• Motivic Geometry Conference, CAS at the Norwegian Academy of Science and Letters, Sep 2020 (online)

• Non-commutative Geometry and Related Topics Conference, CMSA Harvard, Mar 2020

• Algebraic Geometry Seminar, Duke University, Nov 2019

• AMS sectional meeting, UC Riverside, Nov 2019

• Algebraic Geometry Seminar, UC Davis, February 2019