Meetings
Bay Area Differential Geometry Seminar (BADG)
- Stanford, June 2, 2012.
Complex Geometry and Microlocal Analysis - special session in
the AMS Eastern Spring meeting, Boston College, April 6-7, 2013.
Teaching
2011-2012
Undergraduate research project: Optimal Transportation
(SURIM, Summer 2012).
Introduction to Optimal Transportation (course 287, Winter 2012):
MWF 11am.
Linear Algebra and Differential Calculus of Several Variables
(course 51, Autumn 2011):
MWF 11am and 1:15pm.
2009-2010
Partial Differential Equations (course 256A, Spring 2010):
MWF 2:15pm.
Complex Analysis, Geometry, and Topology (course 215A, Autumn 2009):
TTh 2:15pm.
2008-2009
Riemannian Geometry (course 110.645, Fall 2008, at JHU).
Seminars
Geometry Seminar.
Seminars in the Department.
Past Seminars
2008-2009 (JHU):
Complex Geometry Seminar.
Informal graduate student seminar on Kahler geometry through examples.
2005-2006 (MIT):
Graduate Student Seminar on Geometric Stability in Differential
Geometry.
Publications
(with S. Zelditch)
The Cauchy problem for the
homogeneous Monge-Ampere equation, III. Lifespan,
preprint, 2012, arxiv:1205.4793.
(with T.D. Jeffres and R. Mazzeo)
Kahler-Einstein metrics with edge singularities,
(with an appendix by C. Li and Y.A. Rubinstein),
preprint, 2011, arxiv:1105.5216. To appear in Annals of Math.
(with B. Clarke)
Conformal deformations of the Ebin metric and a generalized Calabi metric
on the space of Riemannian metrics,
preprint, 2011, arxiv:1104.4314. To appear in Ann. IHP Anal. Non Lineaire.
(with B. Clarke)
Ricci flow and the metric
completion of the space of Kahler metrics,
preprint, 2011, arxiv:1102.3787. To appear in Amer. J. Math.
(with S. Zelditch)
The Cauchy problem for the
homogeneous Monge-Ampere equation, II. Legendre transform,
Adv. Math. 228 (2011), 2989-3025.
(with S. Zelditch)
The Cauchy problem for the
homogeneous Monge-Ampere equation, I. Toeplitz
quantization, J. Differential Geom. 90 (2012), 303-327.
(with I. Rodnianski and G. Staffilani)
On the global well-posedness of the one-dimensional Schrodinger map
flow, Analysis and PDE 2 (2009), 187-209.
(with S. Zelditch)
Bergman approximations of harmonic maps into the space of Kahler metrics on toric
varieties, J. Symp. Geom. 8 (2010), 239-265.
(alternative link)
Geometric quantization and dynamical constructions on the
space of Kahler metrics, Ph.D. Thesis, Massachusetts Institute of Technology, 2008.
Some discretizations of geometric evolution equations and the Ricci iteration
on the space of Kahler metrics, Adv. Math. 218 (2008), 1526-1565.
On the construction of Nadel multiplier ideal sheaves and the limiting behavior
of the Ricci flow,
Trans. Amer. Math. Soc. 361 (2009), 5839-5850.
The Ricci iteration and its
applications, C. R. Acad. Sci. Paris 345 (2007), 445-448.
On energy
functionals, Kahler-Einstein metrics, and the
Moser-Trudinger-Onofri neighborhood, J. Funct. Anal. 255, special issue
dedicated to Paul Malliavin (2008), 2641-2660.
(with M. Peterson)
Turbulence on a desktop,
Comp. Sci. Eng. 3 (2001), 86-94.
(with S. Gueron)
The minimal reversible coagulation-fragmentation process having no factorized coagulation and
fragmentation rates, Markov Process. Related Fields 6 (2000), 257-264.
(with H. Bailey)
A Variety of Triangle Inequalities,
College Math. J. 31 (2000), 350-355.
Errata list for my articles
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