Sébastien Picard
Assistant Professor
Mathematics Department
University of British Columbia
Email: spicard@math.ubc.ca
Office: MATH 236
Research Interests: Differential geometry, partial differential equations, Calabi-Yau manifolds.
My CV can be found here.
Current Teaching:
o Math 317: Calculus IV (Fall 2023)
o Math 253: Multivariable Calculus (Summer 2023)
Seminars:
o UBC Differential Geometry, Mathematical Physics, and PDE Seminar
Publications and Preprints:
o (with C. Suan and B. Friedman) Gromov-Hausdorff continuity of non-Kahler Calabi-Yau conifold transitions
Preprint 2024 (arxiv)
o The Strominger system and flows by the Ricci tensor
Preprint 2024 (arxiv)
o (with J. McOrist and E.E. Svanes) A heterotic Hermitian-Yang-Mills equivalence
Preprint 2024 (arxiv)
o (with Pei-Lin Wu) Balanced and Aeppli parameters for the heterotic moduli
Preprint 2024 (arxiv)
o (with T.C. Collins and S.-T. Yau) The Strominger system in the square of a Kahler class
To appear in Pure and Applied Mathematics Quarterly (arxiv)
o (with C. Suan) Flows of G2-Structures associated to Calabi-Yau Manifolds
To appear in Math. Res. Lett. (arxiv)
o (with T. Fei, D.H. Phong, X.-W. Zhang) Stability of the Type IIA flow and its applications in symplectic geometry
To appear in Comm. Anal. Geom. (arxiv)
o (with T.C. Collins and S.-T. Yau) Stability of the tangent bundle through conifold transitions
Comm. Pure Appl. Math. 77, 284-371 (2024). (journal, arxiv)
o (with T.C. Collins, S. Gukov, and S.-T. Yau) Special Lagrangian cycles and Calabi-Yau transitions
Commun. Math. Phys. 401, 769–802 (2023). (journal, arxiv)
o (with T. Fei, D.H. Phong, X.-W. Zhang) Bochner-Kodaira formulas and the Type IIA flow
J. Geom. Anal. 33, no. 48 (2023). (journal, arxiv)
o Transitions and Fluxes
Mathematical Research Postcards (2022). (journal)
o (with T. Fei, D.H. Phong, X.-W. Zhang) Estimates for a geometric flow for the Type IIB string
Math. Ann. 382 (2022), 1935-1955. (journal, arxiv)
o (with T.C. Collins) The Dirichlet problem for the k-Hessian equation on a complex manifold
American Journal of Mathematics 144, no. 6 (2022), 1641-1680. (journal, arxiv)
o (with T. Fei, D.H. Phong, X.-W. Zhang) Geometric flows for the Type IIA string
Cambridge Journal of Mathematics, Vol. 9, No. 3 (2021), 683-807. (journal, arxiv)
o (with T. Fei) Anomaly flow and T-duality
Pure and Applied Mathematics Quarterly, Vol. 17, No. 3 (2021), 1083-1112 (journal, arxiv)
o (with D.H. Phong, X.-W. Zhang) Fu-Yau Hessian equations
J. Differential Geom. 118 (2021), no. 1, 147-187. (journal, 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
J. Differential Geom. 117 (2021), no. 1, 23-39. (journal, arxiv)
o (with X.-W. Zhang) Parabolic complex Monge-Ampere equations on compact Kahler manifolds
Proceedings of the International Consortium of Chinese Mathematicians 2018, International Press of Boston (2020). (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. (journal, 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 Course Notes:
o Topics in Complex Geometry
o Differential Geometry II
o Spinors and Non-Kähler Threefolds
o Hölder Estimates for Parabolic PDE
o Calabi-Yau Manifolds with Torsion and Geometric Flows
