Tristan C. Collins
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027 USA
Phone: (212) 854-4112
Email: [email protected]
Education
Ph.D., Mathematics, Columbia University, 2014 (Expected). Advisor: Prof. Duong H. Phong.
M. Phil., Mathematics, Columbia University, 2012
M.A., Mathematics, Columbia University, 2010
B.Sc., Mathematics, University of British Columbia, 2009 (with Honours).
Fields of Interest
Differential Geometry, Partial Differential Equations, Algebraic Geometry, Harmonic Analysis.
Preprints and Publications
10. Poisson metrics on flat vector bundles over non-compact curves (with A. Jacob and S.-T. Yau), preprint
2014
9. An extension theorem for Kähler currents (with V. Tosatti), preprint 2013
8. Kähler currents and null loci (with V. Tosatti), preprint 2013
7. The twisted Kähler-Ricci flow (with G. Székelyhidi), preprint 2012
6. Remarks on the Yang-Mills flow on a compact Kahler manifold (with A. Jacob), preprint 2012
5. K-Semistability for irregular Sasakian manifolds (with G. Székelyhidi), to appear in J. Differential
Geom.
4. On the convergence of the Sasaki-Ricci flow (with A. Jacob), preprint 2011
3. Stability and convergence of the Sasaki-Ricci flow, to appear in J. Reine Angew. Math.
2. Uniform Sobolev inequality along the Sasaki-Ricci flow, Journal of Geometric Analysis (online), 2012
1. The transverse entropy functional and the Sasaki-Ricci flow, Trans. Amer. Math. Soc. 365 (2013),
no. 3, 12771303.
0. A multidimensional resolution of singularities with applications to analysis (with A. Greenleaf, M.
Pramanik), Amer. J. Math. 135 (2013), no. 5, 1179-1252.
Honors, Awards, & Fellowships
NSERC PGS-D scholarship, Columbia University, 2010-2012.
Presidential Fellowship, Columbia University, 2009.
NSERC PGS scholarship, Columbia University, 2009.
Tristan C. Collins
2
NSERC Undergraduate Student Research Award, University of British Columbia, 2008. Critical Integrability Indices of Multivariate Polynomials under the supervision of Malabika Pramanik.
G.C. Webber Memorial Prize in Mathematics, University of British Columbia, 2009.
Conference and Seminar Presentations
City University of New York, January 31, 2012. Geometry and Analysis Seminar.
University of Rochester, February 3, 2012. Analysis and Geometry Seminar.
Northwestern University, October 9, 2012. Geometry and Physics Seminar.
Columbia University, May 8, 2013. Analysis, Complex Geometry, and Mathematical Physics: A Conference in Honor of Duong H. Phong.
Rutgers University, August 12, 2013. Summer School in Complex Geometry.
Johns Hopkins University, September 24, 2013. Complex Geometry Seminar.
University of Connecticut, October 7, 2013. PDE and Differential Geometry Seminar.
Northwestern University, November 15, 2013. Complex Geometry Seminar.
University of New Mexico, April 5-6, 2014. AMS Spring Sectional Meeting: Special Session on Analysis
and Topology in Special Geometries.
Service
Co-organizer of the Special Day on Geometry and PDE, October 26, 2013, Columbia University
Co-organizer of the Informal Complex Geometry and PDE Seminar at Columbia University (2012-present)
Organizer of the Graduate Student Geometric Analysis Seminar, (2011-2013)
Referee for: Journal of the American Mathematical Society, Mathematical Research Letters, Journal für
die reine und angewandte Mathematik.
Teaching
Columbia University
Ordinary Differential Equations, Summer 2012
Ordinary Differential Equations, Summer 2013
Last updated: March 31, 2014