Title: The ultrahyperbolic equation after Fritz John
Speaker: Guillem Cobos, IT Tralee
The talks will be held virtually this semester via Microsoft Teams. Link to join the meeting is given below. All are welcome.
TO JOIN CLICK: Join Microsoft Teams Meeting
NOTE TIME CHANGE TO 4PM
ABSTRACT:
Fritz John showed in 1938 that the ultrahyperbolic equation arises as the compatibility for functions on line space to come from line integrals of functions in Euclidean 3-space. The introduction of the canonical neutral Kaehler metric on the space of oriented lines clarifies the relationship and broadens the paradigm to allow new insights. In particular, conformal maps of the neutral metric are used to generate new solutions to the equation. The link with tomography is explained, and the possibility of image reconstruction from attenuation values along lines intersecting a fixed line in space is discussed.
Image Source - https://commons.wikimedia.org/wiki/File:Pure-mathematics-formul%C3%A6-blackboard.jpg