Tristan C. Collins
Harvard University
Department of Mathematics
One Oxford St., Cambridge, MA 02138
Email: tcollins at math dot harvard dot edu
I am a Benjamin Peirce Assistant Professor in the Mathematics Department at Harvard University. I completed my Ph.D. under the supervision of D.H. Phong at Columbia University in New York City. Before studying at Columbia, I studied mathematics at the University of British Columbia in Vancouver, B.C., where I worked with Malabika Pramanik.
I do research in geometry and analysis. I am particularly interested in geometric flows, and applications of algebraic geometry to analysis, and vice versa.
My research is partially supported by NSF grant DMS-1506652.
Here's my CV last updated September 18, 2017
Teaching
Fall 2017
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Differential Geometry
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Differential Geometry of Curves and Surfaces
Fall 2016
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Differential Geometry
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Analytic Techniques in Algebraic Geometry
Spring 2016
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Introductory Real Analysis
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Nonlinear Elliptic Equations
Fall 2015
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Differential Geometry of Curves and Surfaces
Spring 2015
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Introductory Real Analysis
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The Geometry of the Complex Monge-Ampère Equation
Fall 2014
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Differential Geometry of Curves and Surfaces
Summer 2014
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Ordinary Differential Equations
Publications and Preprints
- (with T. Hisamoto and R. Takahashi) The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
[arXiv] prepreint 2017
- (with D. Xie, and S.-T. Yau) The deformed Hermitian-Yang-Mills equation in geometry and physics
[arXiv] preprint 2017
- Log-canonical thresholds in real and complex dimension 2
[arXiv] preprint 2017
- (with C. Mooney) Dimension of the minimum set for the real and complex Monge-Ampere equations in critical Sobolev spaces
[arXiv] Anal. and PDE 10 (2017), no. 8 2013--2041
- (with V. Tosatti) Restricted volumes on Kahler manifolds
[arXiv] preprint 2016
- (with S. Picard and X. Wu) Concavity of the Lagrangian phase operator and applications
[arXiv] Calc. Var. and Partial Differential Equations 56 (2017), no. 4, Art. 89
- (with D. Xie and S.-T. Yau) K stability and stability of chiral ring
[arXiv] preprint 2016
- (with G. Székelyhidi) Sasaki-Einstein metrics and K-stability
[arXiv] preprint 2015
- (with A. Jacob and S.-T. Yau) (1,1) forms with specified Lagrangian phase.
[arXiv] preprint 2015
- (with A. Jacob and S.-T. Yau) Poisson metrics on flat vector bundles over non-compact curves
[arXiv] to appear in Comm. Anal. Geom.
- (with V. Tosatti) A singular Demailly-Paun theorem
[arXiv] C. R. Math. Acad. Paris 354 (2016), no. 1, 91--95
- C^{2,α} estimates for nonlinear elliptic equations of twisted type
[arXiv] Calc. Var. Partial Differential Equations 55 (2016), no. 1, Art. 6
- (with G. Székelyhidi) Convergence of the J-flow on toric manifolds
[arXiv] J. Differential Geom. 107 (2017), no. 1, 47--81
- (with V. Tosatti) Kahler currents and null loci
[arXiv] Inventiones Math. 202 (2015), no. 3, 1167--1198
- (with G. Székelyhidi) The twisted Kahler-Ricci flow
[arXiv] J. Reine Angew. Math. 716 (2016), 179--205
- (with G. Székelyhidi) K-Semistability for irregular Sasakian manifolds
[arXiv] to appear in the Journal of Differential Geometry
- (with A. Jacob) On the convergence of the Sasaki-Ricci flow
[arXiv] to appear in Contemp. Math.
- Stability and convergence of the Sasaki-Ricci flow
[arXiv] J. Reine Angew. Math. 716 (2016), 1--27
- (with V. Tosatti) An extension theorem for Kahler currents
[arXiv] Ann. Fac. Sci.Toulouse Math. (6) 23 (2014), no. 4, 893-905
- Uniform Sobolev inequality along the Sasaki-Ricci flow
[arXiv][Journal] J. Geom. Anal. 24 (2014), no. 3, 1323-1336
- (with A. Jacob) Remarks on the Yang-Mills flow on a compact Kahler manifold
[arXiv] Univ. Iagel. Acta Math. no. 51 (2013), 17-43.
- The transverse entropy functional and the Sasaki-Ricci flow
[arXiv] Trans. Amer. Math. Soc. 365 (2013), no. 3, 1277-1303
- (with A. Greenleaf and M. Pramanik) A multidimensional resolution of singularities with applications to analysis
[arXiv] American Journal of Mathematics, 135 (2013), 1179-1252.
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