Publications
Book:
Complex Geometry:
arXiv - - Formal structure of scalar curvature in generalized Kahler geometry, joint with V. Apostolov, Y. Ustinovskiy
arXiv - - The Riemannian and symplectic geometry of the space of generalized Kahler structures, joint with V. Apostolov, Y. Ustinovskiy
arXiv - - The generalized Kahler Calabi-Yau problem, joint with V. Apostolov, X. Fu, Y. Ustinovskiy
arXiv - journal - Kahler stability of symplectic forms, joint with G. Tian
arXiv - journal - Variational structure and uniqueness of generalized Kahler-Ricci solitons, joint with V. Apostolov, Y. Ustinovskiy
arXiv - journal - Non-Kahler Calabi-Yau geometry and pluriclosed flow, joint with M. Garcia-Fernandez, J. Jordan
arXiv - journal - Generalized Kahler-Ricci flow on toric Fano varieties, joint with V. Apostolov, Y. Ustinovskiy
arXiv - journal - Ricci-Yang-Mills flow on surfaces and pluriclosed flow on elliptic fibrations
arXiv - journal - The Gibbons-Hawking ansatz in generalized Kahler geometry, joint with Y. Ustinovskiy
arXiv - journal - Deformation classes in generalized Kahler geometry, joint with M. Gibson
arXiv - journal - On a Calabi-type estimate for pluriclosed flow, joint with J. Jordan
arXiv - journal - Classification of generalized Kahler-Ricci solitons on complex surfaces, joint with Y. Ustinovskiy
arXiv - journal - Complex manifolds with negative curvature operator, joint with M.C. Lee
arXiv - journal - Pluriclosed flow and the geometrization of complex surfaces
arXiv - journal - Classification of solitons for pluriclosed flow on complex surfaces
arXiv - journal - The nondegenerate generalized Kahler Calabi-Yau problem, joint with V. Apostolov
arXiv - journal - Global viscosity solutions of generalized Kahler-Ricci flow
arXiv - journal - Pluriclosed flow on manifolds with globally generated bundles
arXiv - journal - Generalized Kahler-Ricci flow and the classification of nondegenerate generalized Kahler surfaces
arXiv - journal - Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kahler structures
arXiv - journal - Evans-Krylov estimates for a nonconvex Monge Ampere equation, joint with M. Warren
arXiv - journal - Pluriclosed flow on generalized Kahler manifolds with split tangent bundle
arXiv - journal - Generalized Kahler Geometry and the Pluriclosed Flow, joint with G. Tian
arXiv - journal - Symplectic curvature flow, joint with G. Tian
arXiv - journal - Regularity results for pluriclosed flow, joint with G. Tian
arXiv - journal - A parabolic flow of pluriclosed metrics, joint with G. Tian
arXiv - journal - Hermitian Curvature Flow, joint with G. Tian
Higher-order equations:
arXiv - journal - A concentration-collapse decomposition for L^2 flow singularities
arXiv - journal - The consistency and convergence of K-energy minimizing movements
arXiv - journal - Long time existence of minimizing movement solutions of Calabi flow
arXiv - journal - The long time behavior of fourth order curvature flows
arXiv - journal - The gradient flow of the L^2 curvature energy on surfaces
arXiv - journal - The gradient flow of the L^2 curvature energy near the round sphere
- journal - The gradient flow of the L^2 curvature functional with small initial energy
arXiv - journal - Asymptotic curvature decay and removal of singularities of Bach-flat metrics
- journal - The Gradient Flow of $\int_M |\Rm|^2$
Geometric equations in mathematical physics:
arXiv - - Ricci flow on Courant algebroids, joint with C. Strickland-Constable, F. Valach
arXiv - journal - Optimal transport and generalized Ricci flow, joint with E. Kopfer
arXiv - journal - Scalar curvature, entropy, and generalized Ricci flow
arXiv - journal - Bochner formulas, functional inequalities and generalized Ricci flow, joint with E. Kopfer
arXiv - journal - Four-dimensional generalized Ricci flows with nilpotent symmetry, joint with S. Gindi
arXiv - journal - Codimension four regularity of generalized Einstein structures, joint with X. Fu, A. Naber
arXiv - journal - Structure of collapsing solutions of generalized Ricci flow, joint with S. Gindi
arXiv - journal - Singularity formation in the Yang-Mills flow, joint with C. Kelleher
arXiv - journal - Entropy, stability, and harmonic map flow, joint with J. Boling, C. Kelleher
arXiv - journal - Entropy, stability, and Yang-Mills flow, joint with C. Kelleher
arXiv - journal - Generalized geometry, T-duality, and renormalization group flow
arXiv - journal - Parabolic optimal transport equations on manifolds, joint with Y.H. Kim, M. Warren
- journal - Singularities of renormalization group flows
- journal - Regularity and expanding entropy for connection Ricci flow
- journal - Quasi-local mass functionals and generalized inverse mean curvature flow
Conformal geometry:
arXiv - journal - Index-energy estimates for Yang-Mills connections and Einstein metrics, joint with C. Kelleher, M. Gursky
arXiv - journal - A conformally invariant gap theorem in Yang-Mills theory, joint with C. Kelleher, M. Gursky
arXiv - journal - Variational structure of the v_{n/2} Yamabe problem, joint with M. Gursky
arXiv - journal - A formal Riemannian structure on conformal classes and uniqueness for the \sigma_2 Yamabe problem, joint with M. Gursky
arXiv - journal - A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow, joint with M. Gursky
Information geometry: