A nonlinear Plancherel Theorem with applications to global well-posedness for the defocusing Davey-Stewartson equation and to the Calderón inverse problem in dimension 2

Speaker: 

Adrian Nachman

Institution: 

University of Toronto, Canada

Time: 

Thursday, April 23, 2020 - 9:00am to 10:00am

Host: 

Katya Krupchyk

Location: 

Zoom

https://sites.uci.edu/inverse/

A hybrid inverse problem of fluorescence ultrasound modulated optical tomography in the diffusive regime

Speaker: 

Yimin Zhong

Speaker Link: 

https://sites.google.com/view/zhongyimin

Institution: 

UCI

Time: 

Friday, January 24, 2020 - 4:00pm to 4:50pm

Location: 

RH 306

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the boundary measurement of the photon currents allows unique and stable reconstructions of the absorption coefficient of the fluorophores at the excitation frequency and the quantum efficiency coefficient simultaneously, provided that some background medium parameters are known. Reconstruction algorithms are proposed and numerically implemented as well.

Geodesic X-Ray Transform on Asymptotically Hyperbolic Manifolds

Speaker: 

Nikolas Eptaminitakis

Speaker Link: 

http://sites.math.washington.edu/~neptamin/

Institution: 

University of Washington

Time: 

Friday, February 7, 2020 - 4:00pm to 4:50pm

Host: 

Katya Krupchyk

Location: 

RH 306

Asymptotically hyperbolic manifolds are a class of non-compact, complete manifolds whose behavior near infinity resembles in many ways that of hyperbolic space. In part due to the behavior of geodesics and their infinite length, and the fact that those spaces have infinite volume, the study of the geodesic X-ray transform becomes particularly interesting and challenging. In this talk we will discuss the problem of injectivity of the geodesic X-ray transform on asymptotically hyperbolic manifolds, identify the issues induced by the geometry, and present some progress in extending to this setting the celebrated local injectivity result proved by Uhlmann and Vasy on compact manifolds with boundary. Joint work with Robin Graham.

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