Inverse problems for fractional operators

Speaker: 

Li Li

Institution: 

UC Irvine

Time: 

Friday, December 9, 2022 - 2:00pm to 2:50pm

Host: 

Katya Krupchyk

Location: 

RH 510R

I will talk about several uniqueness results for inverse problems. I will first review the classical Calderón problem. Then I will focus on the fractional Calderón problem and its evolutionary and nonlinear variants. The goal is to determine nonlinearities/coefficients in fractional equations from exterior partial measurements of the Dirichlet-to-Neumann map.

Travel time inverse problems on simple Riemannian manifolds

Speaker: 

Boya Liu

Institution: 

NC State

Time: 

Thursday, December 8, 2022 - 5:00pm to 5:50pm

Host: 

Katya Krupchyk

Location: 

RH 306

We provide new proofs based on the Myers--Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics. This is joint work with Joonas Ilmavirta and Teemu Saksala.

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