**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 529: Differential Topology (Fall 2024)

** o **Math 425/525: Differential Geometry I (Fall 2024)

** o **Math 253: Multivariable Calculus (Summer 2024)

**Seminars:**

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

**Publications and Preprints:**

** o ** (with B. Chisamanga, J. McOrist and E.E. Svanes) *The decoupling of moduli about the standard embedding*

Preprint 2024 (arxiv)

** o ** (with C. Suan and B. Friedman) *Gromov-Hausdorff continuity of non-Kahler Calabi-Yau conifold transitions*

Preprint 2024 (arxiv)

** o ** (with J. McOrist and E.E. Svanes) *A heterotic Hermitian-Yang-Mills equivalence*

Preprint 2024 (arxiv)

** o ** *The Strominger system and flows by the Ricci tensor*

To appear in Surveys in Differential Geometry (arxiv)

** o ** (with Pei-Lin Wu) *Balanced and Aeppli parameters for the heterotic moduli*

To appear in International Journal of Mathematics (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 ** TIMS mini-course on the Strominger system: **1**,**2**,**3**,**4**,**5**

** o ** Calabi-Yau Manifolds with Torsion and Geometric Flows

** o ** Spinors and Non-Kähler Threefolds

** o ** Topics in Complex Geometry

** o ** Differential Geometry II

** o ** Hölder Estimates for Parabolic PDE