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.

Reconstruction of a manifold from travel time data

Speaker: 

Teemu Saksala

Institution: 

NC State

Time: 

Thursday, December 8, 2022 - 4:00pm to 4:50pm

Host: 

Katya Krupchyk

Location: 

RH 306

In this talk I will introduce two geometric datasets given by the distance function on a Riemannian manifold with boundary. For each of these data sets I will provide geometric conditions that are sufficient to determine the isometry class of the manifold producing the data.  This talk is based on joint works with Maarten V. de Hoop, Joonas Ilmavirta, Matti Lassas and Ella Pavlechko.

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