The VI AMMCS International Conference
Waterloo, Ontario, Canada | August 14-18, 2023
AMMCS 2023 Plenary Talk
The isometric immersions problem: from perspectives of PDE, geometry, and physics
Siran Li (Shanghai Jiao Tong & New York University)
We report our recent work on a classical problem in differential geometry: isometric immersions and/or embeddings of Riemannian and semi-Riemannian manifolds. The underlying
PDE is the system of Gauss-Codazzi-Ricci equations. Existence of isometric immersions is
studied under various curvature conditions, via elliptic and hyperbolic PDE techniques. Weak
continuity of isometric immersions is investigated with the help of the theory of compensated
compactness. Connections to other problems in mathematical physics, including fluid dynamics,
harmonic maps, and Coloumb gauges, will be discussed.
Our talk contains joint work with Gui-Qiang Chen, Reza Pakzad, Armin Schikorra, and Marshall Slemrod.
Our talk contains joint work with Gui-Qiang Chen, Reza Pakzad, Armin Schikorra, and Marshall Slemrod.
Siran Li grew up in Beijing, studied mathematics from 2009 to 2013 at Columbia University,
New York, and obtained the D.Phil. degree in 2017 from the University of Oxford, under the
supervision of Gui-Qiang Chen. He did postdoctoral researches with Bob Hardt from 2017
to 2020 at Rice University, Houston, and spent the year 2018 - 2019 at McGill and Concordia
Universities in Montreal as a CRM-ISM postdoctoral fellow. Siran moved back to China in 2020,
first working at New York University-Shanghai. He joined Shanghai Jiao Tong University as an
associate professor in September 2021.
Siran's main research interests include analysis of partial differential equations, geometric
measure theory, and applied mathematics. One of the main themes of his mathematical work
is the analysis of singularities, or structures of weak regularities, which arise naturally from
problems in differential geometry and fluid dynamics. His recent research projects concern with
isometric immersions of manifolds, the theory of compensated compactness, and the Navier-Stokes equations.
Recorded talk of Dr. Siran Li can be found here