The Calderon Problem for Connections: Two Perspectives

Abstract

The speaker considers the problem of identifying a unitary connection \nabla on a vector bundle, up to gauge equivalence, from the Dirichlet-to-Neumann map of the connection Laplacian \nabla^*\nabla. One possible approach is through the construction of special Complex Geometric Optics solutions and a further reduction of the problem to an X-ray transform. The speaker also considers another approach in the Yang-Mills connections setting, based on picking a special gauge, in which the Yang-Mills equations become elliptic and using a unique continuation principle for elliptic systems for identification near the boundary.

About the speaker

Dr. Mihajlo Cekić obtained his PhD in Mathematics from the University of Cambridge in 2017. He is currently a Postdoctoral Fellow at the Max-Planck Institute for Mathematics in Bonn, Germany. His research interests are mainly geometric inverse problems.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.