Books
M.A. Peterson, Y.A. Rubinstein, Eds.,
Directions for Mathematics Research Experience for Undergraduates, World Scientific, 2016.
(book
review in Notices of the American Mathematical Society,
book
review in The Mathematical Gazette)
Meetings
Metro Area Differential Geometry Seminar (MADGuyS)

University of Maryland, May 4, 2018.
UMD Geometry Week

University of Maryland,
1216 March 2018.
Maryland Analysis and Geometry Atelier

University of Maryland,
2125 August 2017.
Videos of lectures
Pacific Rim Workshop on Geometric Analysis
 University of British Columbia, July 2428, 2017.
New Directions for Mathematics Research Experiences for Undergraduates
 Mt. Holyoke College, June 2122, 2013.
28th Geometry Festival: Calabifest 
In celebration of the 90th birthday of Eugenio Calabi,
University of Maryland,
April 1214, 2013.
Complex Geometry and Microlocal Analysis  special session at
the AMS Eastern Spring meeting, Boston College, April 67, 2013.
Bay Area Differential Geometry Seminar (BADG)
 Stanford, June 2, 2012.
Minicourses
SCGAS
Winter School
 UC Irvine, January 2529, 2016.
Getting
Started with PDEs
 IIAS, Hebrew University, September 39, 2015.
Advanced School on PDEs in Geometry and Physics
 Hefei, China, June 30July 11, 2014.
Seminars
JHUUMD
Complex Geometry Seminar
Informal
Geometric Analysis Seminar
Seminars in the Department.
Teaching
20172018
Differential
Equations for Scientists and Engineers (honors)
(course 246H, Spring 2018):
TuTh 12:30pm, MATH 1308.
Geometric Analysis
(course 742, Fall 2017):
TTh 2pm, MATH B0431.
20162017
Differential
Equations for Scientists and Engineers (honors)
(course 246H, Spring 2017):
TuTh 12:30pm, MATH 1308.
Differential
Equations for Scientists and Engineers (honors)
(course 246H, Fall 2016):
TuTh 12:30pm, MATH 0304.
20152016
Differential
Equations for Scientists and Engineers (honors)
(course 246H, Fall 2015):
MWF 10am, MATH 1311.
Topics in fully nonlinear
PDE
(course 858Y, Fall 2015):
MWF 12 noon, MATH 1313.
20142015
Geometric Analysis
(course 742, Fall 2014):
TTh 9:30am, MATH 0104.
Topics in Complex Analysis: Kahler
Manifolds
(course 868K, Fall 2014):
TTh 12:30am, EGR 3114.
20132014
Geometric Analysis
(course 742, Fall 2013):
TTh 11am, MATH 1308.
Differential Geometry of
Curves and
Surfaces I
(course 436, Fall 2013):
TTh 2pm, MATH B0421.
20122013
Topics in
Geometric Analysis: The Yamabe Problem
(course 748F, Spring 2013):
TTh 2pm.
Geometry
(course 430, Fall 2012):
TTh 2pm.
20112012
Undergraduate
research project: Optimal Transportation
(SURIM, Summer 2012).
Introduction
to Optimal Transportation (course 287, Winter 2012, at Stanford):
MWF 11am.
Linear
Algebra and Differential Calculus of Several Variables
(course 51, Autumn 2011, at Stanford):
MWF 11am and 1:15pm.
20092010
Partial
Differential Equations (course 256A, Spring 2010, at Stanford):
MWF 2:15pm.
Complex
Analysis, Geometry, and Topology (course 215A, Autumn 2009, at Stanford):
TTh 2:15pm.
20082009
Riemannian
Geometry (course 110.645, Fall 2008, at JHU).
Past Seminars
20092012 (Stanford):
Geometry Seminar.
20082009 (JHU):
Complex
Geometry Seminar.
Informal
graduate student seminar on Kahler geometry through examples.
20052006 (MIT):
Graduate
Student Seminar on Geometric
Stability in Differential
Geometry.
Publications
(with I.A. Cheltsov, K. Zhang)
Basis log canonical thresholds, local intersection estimates, and
asymptotically log del Pezzo surfaces,
preprint, 2018, arxiv:1807.07135.
Tian's
properness conjectures: an introduction to Kahler geometry,
preprint, 2018, arxiv:1807.00928.
(with T. Darvas, C.H. Lu)
Quantization in geometric pluripotential theory,
preprint, 2018, arxiv:1806.03800.
(with T. Darvas)
Convergence of the KahlerRicci iteration,
Analysis and PDE 12 (2019), 721735.
(with B. Berndtsson, D. CorderoErausquin, B. Klartag)
Complex Legendre duality,
preprint, 2016, arxiv:1608.05541.
(with B. Berndtsson, D. CorderoErausquin, B. Klartag)
Complex interpolation of Rnorms, duality and foliations,
preprint, 2016, arxiv:1607.06306.
(with T. Darvas)
A minimum principle for Lagrangian graphs,
preprint, 2016, arxiv:1606.08818.
(with A. Pulemotov)
Ricci iteration on homogeneous spaces,
preprint, 2016, arxiv:1606.05064.
(with M. Lindsey)
Optimal transport via a MongeAmpère optimization problem
,
SIAM J. Math. Anal. 49 (2017), 30733124.
(with I.A. Cheltsov)
On flops and canonical metrics,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), 283–311.
(with J.P. Solomon)
The
degenerate special Lagrangian equation,
Adv. Math. 310 (2017), 889939.
(with T. Darvas)
Tian's properness conjectures and Finsler geometry of the space of Kahler
metrics,
J. Amer. Math. Soc. 30 (2017), 347387.
(with R. Vakil)
REUs with limited faculty involvement, "underrepresented" subjects in the
undergraduate curriculum, and the culture of Mathematics,
in:
Directions for Mathematics Research Experience for Undergraduates
(M.A. Peterson, Y.A. Rubinstein, Eds.), World Scientific, 2016,
pp. 5372.
(with T. Darvas)
Kiselman's principle, the Dirichlet problem for the MongeAmpere equation, and
rooftop obstacle problems
(alternative link),
J. Math. Soc. Japan 68 (2016), 773–796.
Smooth
and singular KahlerEinstein metrics
in:
Geometric and Spectral Analysis
(P. Albin et al., Eds.),
Contemp. Math. 630, AMS and Centre Recherches Mathematiques, 2014,
pp. 45138.
(with A. Carlotto and O. Chodosh)
Slowly converging Yamabe flows,
Geom. & Top. 19 (2015), 15231568.
(with O. Chodosh, V. Jain, M. Lindsey, and L. Panchev)
On discontinuity of planar optimal transport maps ,
J. Topology & Analysis 7 (2015), 239260.
(with S. ArtsteinAvidan)
Differential analysis of polarity: Polar HamiltonJacobi,
conservation laws, and Monge Ampère equations,
J. d'Analyse Math. 132 (2017),
133156.
(with I.A. Cheltsov)
Asymptotically log Fano varieties,
Adv. Math. 285 (2015), 12411300.
(with R. Mazzeo and N. Sesum)
Ricci flow on surfaces with conic singularities,
Analysis and PDE 8 (2015), 839882.
(with R. Mazzeo)
The Ricci continuity method for the complex MongeAmpere equation,
with applications to KahlerEinstein edge metrics,
C. R. Math. Acad. Sci. Paris 350 (2012), 693697.
(with S. Zelditch)
The Cauchy problem
for the homogeneous MongeAmpere equation, III. Lifespan,
Crelle's J. 724 (2017), 105143.
(with R. Mazzeo and T. Jeffres)
KahlerEinstein metrics with edge singularities,
(with an appendix by C. Li and Y.A. Rubinstein),
Annals of Math. 183 (2016), 95176.
(with B. Clarke)
Conformal deformations of the Ebin metric and a generalized Calabi metric
on the space of Riemannian metrics,
Ann. IHP Anal. Non Lineaire 30 (2013), 251274.
(with B. Clarke)
Ricci flow and the metric
completion of the space of Kahler metrics,
Amer. J. Math. 135 (2013), 14771505.
(with S. Zelditch)
The Cauchy problem for the
homogeneous MongeAmpere equation, II. Legendre transform,
Adv. Math. 228 (2011), 29893025.
(with S. Zelditch)
The Cauchy problem for the
homogeneous MongeAmpere equation, I. Toeplitz
quantization, J. Differential Geom. 90 (2012), 303327.
(with I. Rodnianski and G. Staffilani)
On the global wellposedness of the onedimensional Schrodinger map
flow, Analysis and PDE 2 (2009), 187209.
(with S. Zelditch)
Bergman approximations of harmonic maps into the space of Kahler metrics on toric
varieties, J. Symp. Geom. 8 (2010), 239265.
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), 15261565.
On the construction of Nadel multiplier ideal sheaves and the limiting behavior
of the Ricci flow,
Trans. Amer. Math. Soc. 361 (2009), 58395850.
The Ricci iteration and its
applications, C. R. Acad. Sci. Paris 345 (2007), 445448.
On energy
functionals, KahlerEinstein metrics, and the
MoserTrudingerOnofri neighborhood, J. Funct. Anal. 255, special issue
dedicated to Paul Malliavin (2008), 26412660.
(with M. Peterson)
Turbulence on a desktop,
Comp. Sci. Eng. 3 (2001), 8694.
(with S. Gueron)
The minimal reversible coagulationfragmentation process having no factorized coagulation and
fragmentation rates, Markov Process. Related Fields 6 (2000), 257264.
(with H. Bailey)
A Variety of Triangle Inequalities,
College Math. J. 31 (2000), 350355.
Errata list for my articles
