PIMS - UCalgary Geometric Analysis Seminar Series: Lili Yan

  • Date: 02/18/2022
  • Time: 14:00
Lili Yan, University of California at Irvine



Abstract: In an inverse boundary problem, one seeks to determine the coefficients of a PDE inside a domain, describing internal properties, from the knowledge of boundary values of solutions of the PDE, encoding boundary measurements. Applications of such problems range from medical imaging to non-destructive testing. In this talk, starting with the fundamental Calderon inverse conductivity problem, we shall first discuss inverse boundary problems for first order perturbations of biharmonic operators in the setting of compact Riemannian manifolds with boundary. Specifically, we shall present a global uniqueness result as well as a reconstruction procedure for the latter inverse boundary problem on conformally transversally anisotropic Riemannian manifolds of dimensions three and higher. Finally, we shall also discuss briefly inverse boundary problems for nonlinear magnetic Schroedinger operators on a compact complex manifold, illustrating the recent insight that the presence of nonlinearity may help when solving inverse problems.


Speaker Biography: Lili Yan is currently a PhD candidate at the University of California, Irvine. Her PhD supervisor is Katya Krupchyk. Lili's research interests are in the field of partial differential equations, inverse problems, and semiclassical analysis.



Other Information: 

This seminar is available via Zoom. Registration is required


Time: 2–3pm PST (3–4pm MDT) 



This seminar series will promote mathematical and physical topics employing the use and creation of geometric analysis techniques. Some of the main themes the seminar will explore are 1) PDEs on manifolds, 2) geometric flows, 3) inverse problems for PDEs and geometric settings, and 4) the introduction of microlocal techniques to a broader geometric and analysis audience.


The series will run on Friday afternoons 2–3pm PST (3–4pm MDT), starting January 14, 2022 and ending around April 8, 2022.


See more information and other dates in the series or contact Tracey Balehowsky, tracey.balehowsky@ucalgary.ca