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. I am interested in the limiting properties of the Yang-Mills flow, singularities and defomations of the Yang-Mills equations, 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 August, 2018
• MAT-21A: Differential Calculus
• MAT-141: Euclidean Geometry
• MAT-240B: Differential Geometry
Publications and Preprints
- (with Ved Datar) Hermitian Yang-Mills connections on collapsing elliptically fibered K3 surfaces
- (with T.C. Collins and S.-T. Yau) (1,1) forms with specified Lagrangian phase
- (with T. Walpuski) Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kahler manifolds
[arXiv] Comm. Partial Differential Equations (to appear)
- (with H. Sa Earp and T. Walpuski) Tangent cones of Hermitian Yang-Mills connections with isolated singularities
[arXiv] Math. Res. Lett. (to appear).
- (with T.C. Collins and S.-T. Yau) Poisson metrics on flat vector bundles over non-compact curves
[arXiv] Comm. Anal. Goem. (to appear)
- (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.