University of California Davis

Department of Mathematics

Email: ajacob at math dot ucdavis dot edu

Office: MSB 2111

**Research Interests**

Here's my CV, last updated June, 2017

• MAT-240B: Differential Geometry

- (with T. Walpuski)
*Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kahler manifolds*

[arXiv] preprint 2016.

- (with T.C. Collins and S.-T. Yau)
*(1,1) forms with specified Lagrangian phase*

[arXiv] preprint 2015.

- (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*

[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).

*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.