University of California Davis
Department of Mathematics
Email: ajacob at math dot ucdavis dot edu
Office: MSB 2111
My primary research interests are differential geometry and partial differential equations. Particular topics include the Yang-Mills flow in complex geometry, singularities and defomations of the Yang-Mills equations, the deformed Hermitian-Yang-Mills equation, special Lagrangian equations, and mirror symmetry.
My research is funded in part by a grant from the Simons Foundation.
Here's my CV, last updated July, 2022.
• MAT-21D: Vector Analysis
• MAT-201A: Analysis
Publications and Preprints
- The Deformed Hermitian-Yang-Mills Equation and Level Sets of Harmonic Polynomials
- (with T.C. Collins and Y.-S. Lin) The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces
- (with N. Sheu) The deformed Hermitian-Yang-Mills equation on the blowup of P^n
- (with T.C. Collins and Y.-S. Lin) The Torelli Theorem for ALH* Gravitational Instantons
[arXiv] Forum Math. Sigma (to appear).
- (with V. Datar) Hermitian Yang-Mills connections on collapsing elliptically fibered K3 surfaces
[arXiv] J. Geom. Anal. 32 (2022), no. 2, Paper No. 69, 30pp.
- (with T.C. Collins and Y.-S. Lin) Special Lagrangian submanifolds of log Calabi-Yau manifolds
[arXiv] Duke Math. J. 170 (2021), no. 7, 1291-1375.
- (with V. Datar and Y. Zhang) Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces
[arXiv] J. Differential Geom. 118 (2021), no. 2, 223-296.
- Weak Geodesics for the deformed Hermitian-Yang-Mills equation
[arXiv] Pure Appl.
Math. Q. 17 (2021), no. 3, 1113-1137.
- (with T.C. Collins and S.-T. Yau) (1,1) forms with specified Lagrangian phase: A priori estimates and algebraic obstructions
[arXiv] Camb. J. Math. 8 (2020), no. 2, 407-452.
- (with T.C. Collins and S.-T. Yau) Poisson metrics on flat vector bundles over non-compact curves
[arXiv] Comm. Anal. Geom. 27 (2019), no. 3, 529-597.
- (with T. Walpuski) Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kahler manifolds
[arXiv][Journal] Comm. Partial Differential Equations, 43 (2018), no. 11, 1566-1598.
- (with H. Sa Earp and T. Walpuski) Tangent cones of Hermitian Yang-Mills connections with isolated singularities
[arXiv][Journal] Math. Res. Lett. 25 (2018), no. 5, 1429-1445.
- (with S.-T. Yau) A special Lagrangian type equation for holomorphic line bundles
[arXiv][Journal] Math. Ann. 369 (2017). no 1-2, 869-898
- The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds
[arXiv][Journal] Amer. J. Math. 138 (2016), no. 2, 329-365.
- The limit of the Yang-Mills flow on semi-stable bundles
[arXiv][Journal] J. Reine Angew. Math. 709 (2015), 1-13.
- Stable Higgs bundles and Hermitian-Einstein metrics on non-Kahler manifolds
[arXiv] Analysis, Complex Geometry, and Mathematical Physics: A conference in honor of D. H. Phong, 117-140, Contemp. Math., 644, Amer. Math. Soc., Providence, RI, (2015).
- (with T.C. Collins) On the convergence of the Sasaki-Ricci flow
Analysis, Complex Geometry, and Mathematical Physics: A conference in honor of D. H. Phong, 117-140, Contemp. Math., 644, Amer. Math. Soc., Providence, RI, (2015).
- Existence of approximate Hermitain-Einstein structures on semi-stable bundles
[arXiv][Journal] Asian J. Math. 18 (2014), No. 5, 859-884.
- (with I. Biswas, S. Bradlow and M. Stemmler) Automorphisms and connections on Higgs bundles over compact Kahler manifolds
[Journal] Differential Geom. Appl. 32 (2014), 139-152.
- (with T.C. Collins) Remarks on the Yang-Mills flow on a compact Kahler manifolds
[arXiv] Univ. Iagel. Acta Math. No. 51 (2013), 17-43.
- (with I. Biswas, S. Bradlow and M. Stemmler) Approximate Hermitian-Einstein connections on principal bundles over a compact Riemann surface
[Journal] Ann. Global Anal. Geom. 44 (2013), no. 3, 257-268.
- (with I. Biswas and M. Stemmler) Existence of approximate Hermitian-Einstein structures on semistable principal bundles
[arXiv][Journal] Bull. Sci. Math. 136 (2012), no. 7, 745-751.
- (with C. Carroll, C. Quinn and R. Walters) The isoperimetric problem on planes with density
[Journal] Bull. Austral. Math. Soc. 78 (2008), 177-197.