Dr. Yavar Kian, gave a lecture titled “Around the Calderón problem in a waveguide” at AMSS on 23, April 2018. 

Let $\Omega$ is an unbounded domain of $\mathbb R^3$ associated with a closed waveguide in the sense that there exists $\omega$ a bounded domain of $\mathbb R^2$ such that $\Omega\subset\omega\times\mathbb R$. In this talk, they would consider the inverse problem of determining the magnetic field associated with the magnetic potential $A\in L^\infty(\Omega)^3$ and the electric potential $q\in L^\infty(\Omega;\mathbb C)$ appearing in the magnetic Schröinger equation $\Delta_Au+qu=0$ on $\Omega$, where $\Delta_A$ denotes the magnetic Laplacian defined by $\Delta_A= \Delta+2iA(x)\cdot\nabla +i\textrm{div}_x(A)-|A|^2$, from some data equivalent to observations of solutions on some parts of the boundary $\partial\Omega$.   

Dr. Yavar Kian received his PhD degree in Applied Mathematics from the University of Bordeaux, France, in 2010. He is currently an Assistant Professor at the University of Aix-Marseille, France. He joined the University of Aix-Marseille on 2011. His current research interests include: inverse problems for different PDEs (parabolic, hyperbolic, Schr?dinger and elliptic equations), inverse spectral problems, inverse problems on manifolds, inverse and direct problems for fractional diffusion equations.