Sebastien Picard

Email: spicard@math.harvard.edu
Office: 235 Science Center

About: I am a Benjamin Peirce Fellow at Harvard University. I completed my PhD at Columbia University in 2018 under the supervision of D.H. Phong. My mathematical interests are differential geometry and PDE.

My CV can be found here.

Teaching:
Math 230A: Differential Geometry (Fall 2019)
Math 136: Differential Geometry (Fall 2019)

Publications and Preprints:
o (with T. Collins) The Dirichlet problem for the k-Hessian equation on a complex manifold
Preprint 2019 (arxiv)

o (with X.-W. Zhang) Parabolic complex Monge-Ampere equations on compact Kahler manifolds
Preprint 2019 (arxiv)

o (with T. Fei) Anomaly flow and T-duality
Preprint 2019 (arxiv)

o (with D.H. Phong, X.-W. Zhang) A flow of conformally balanced metrics with Kahler fixed points
To appear in Math. Ann. (journal, arxiv)

o (with T. Fei, Z. Huang) The Anomaly flow over Riemann surfaces
To appear in International Mathematics Research Notices (journal, arxiv)

o (with T. Fei, Z. Huang) A construction of infinitely many solutions to the Strominger system
To appear in Journal of Differential Geometry (arxiv)

o (with D.H. Phong, X.-W. Zhang) Fu-Yau Hessian equations
To appear in Journal of Differential Geometry (arxiv)

o (with D.H. Phong, X.-W. Zhang) The Anomaly flow on unimodular Lie groups
To appear in Contemp. Math. (arxiv)

o (with D.H. Phong, X.-W. Zhang) On estimates for the Fu-Yau generalization of a Strominger system
J. Reine Angew. Math (2019), No. 751, 243-274. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) Anomaly flows
Comm. Anal. Geom. 26 (2018), no. 4, 955-1008. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) The Anomaly flow and the Fu-Yau equation
Annals of PDE 4 (2018), no. 2. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) Geometric flows and Strominger systems
Math. Z. 288 (2018), 101-113. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) New curvature flows in complex geometry
Surveys in Differential Geometry 22 (2017), No. 1, 331-364. (journal, arxiv)

o (with T. Collins, X. Wu) Concavity of the Lagrangian phase operator and applications
Calc. Var. Partial Differential Equations 56 (2017), no. 4, Art. 89 (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) The Fu-Yau equation with negative slope parameter
Invent. Math. 209 (2017), no. 2, 541-576. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) A second order estimate for general complex Hessian equations
Analysis and PDE 9 (2016), no. 7, 1693-1709. (journal, arxiv)

o A priori estimates of the degenerate Monge-Ampere equation on Kahler manifolds of nonnegative bisectional curvature
Math. Res. Lett. 20 (2013), no. 6, 1145-1156. (journal, arxiv)

Lecture Notes:
o Holder Estimates for Parabolic PDE
Part of a course on PDE taught at Harvard in 2019

o Calabi-Yau Manifolds with Torsion and Geometric Flows
Course given at CIME Summer School in 2018

Seminars:
Harvard Differential Geometry Seminar
Open Neighborhood Seminar
BHMN Joint Colloquium