Adam Jacob

Professor

University of California Davis
Department of Mathematics

Email: ajacob at math dot ucdavis dot edu

Office: MSB 2111

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Research Interests

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 deformations of the Yang-Mills equations, the deformed Hermtian-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 June, 2019

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Teaching

Fall 2023

• MAT-218: Partial Differential Equations

• MAT-21A: Differential Calculus

Winter 2024

• MAT-141: Euclidean Geometry

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Publications and Preprints

• (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.
  
  
• (with V. Datar) Hermitian Yang-Mills connections on collapsing elliptically fibered K3 surfaces
  [arXiv] J. Geom. Anal. (to appear).
  
  
• (with T.C. Collins and S.-T. Yau) (1,1) forms with specified Lagrangian phase
  [arXiv] Camb. J. Math. 8 (2020), no. 2, 407-452.
  
  
• Weak Geodesics for the deformed Hermitian-Yang-Mills equation
  [arXiv] Pure Appl. Math. Q. (to appear)
  
  
• (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
  [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.