Research Interests: 

Derived category of coherent sheaves on surfaces and 3-folds. 

• Bridgeland stability condition

• Motivic Donaldson-Thomas theory

Publications and Preprints: 

Bridgeland stability condition:

• 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, submitted.

Motivic Donaldson-Thomas theory:

• Moduli of sheaves on fourfolds as derived Lagrangian intersections, (with Nachiketa Adhikari), arXiv:2403.00727, submitted.

• 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) 

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

Survey articles:

• 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  

Invited Talks:

• Algebraic Geometry Seminar, Univeristy 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