Sébastien Picard

Assistant Professor
Mathematics Department
University of British Columbia


Email: spicard@math.ubc.ca
Office: MATH 236

Research Interests: Differential geometry, geometric analysis, partial differential equations, and complex geometry.

My CV can be found here.


Current Teaching:
o Math 104: Differential Calculus with Applications to Commerce and Social Sciences (Fall 2020)
o Math 317: Calculus IV (Winter 2021)


Publications and Preprints:

o (with T.C. Collins and S.-T. Yau) Stability of the tangent bundle through conifold transitions
Preprint 2021 (arxiv)

o (with T. Fei, D.H. Phong, X.-W. Zhang) Bochner-Kodaira formulas and the Type IIA flow
Preprint 2020 (arxiv)

o (with T. Fei, D.H. Phong, X.-W. Zhang) Geometric flows for the Type IIA string
Preprint 2020 (arxiv)

o (with T. Fei, D.H. Phong, X.-W. Zhang) Estimates for a geometric flow for the Type IIB string
Preprint 2020 (arxiv)

o (with T.C. Collins) The Dirichlet problem for the k-Hessian equation on a complex manifold
To appear in Amer. J. Math. (arxiv)

o (with X.-W. Zhang) Parabolic complex Monge-Ampere equations on compact Kahler manifolds
To appear in Proceedings of the ICCM (arxiv)

o (with T. Fei) Anomaly flow and T-duality
To appear in Pure Appl. Math. Q. (arxiv)

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

o (with T. Fei, Z. Huang) The Anomaly flow over Riemann surfaces
International Mathematics Research Notices 2021, no. 3 (2021), 2134-2165. (journal, arxiv)

o (with T. Fei, Z. Huang) A construction of infinitely many solutions to the Strominger system
Journal of Differential Geometry 117 (2021), no. 1, 23-39. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) A flow of conformally balanced metrics with Kahler fixed points
Math. Ann. 374 (2019), no. 3-4, 2005-2040. (journal, arxiv)

o (with D.H. Phong, X.-W. Zhang) The Anomaly flow on unimodular Lie groups
Contemp. Math. (2019), Volume 735, 217-239. (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.C. 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)


Graduate Topics Course Notes:

o Holder Estimates for Parabolic PDE
Part of a graduate course on PDE

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


Seminars:

o UBC Differential Geometry, Mathematical Physics, and PDE Seminar
o Geometry and TACoS