This talk will focus on using the Euclidean Signature to determine whether two smooth planar curves are congruent under the Special Euclidean group. Work done by Emilio Musso and Lorenzo Nicolodi emphasizes that signatures must be used with caution by constructing 1-parameter families of non-congruent curves with degenerate vertices (curve segments of constant curvature) with identical signatures. We address the claim…

I give an introductory talk about geometric inverse problems and ray transforms (no proofs are involved). I mainly focus on the Euclidean X-ray transform of scalar fields and vector fields, but also introduce the basic properties of the X-ray transform of higher order tensor fields. I give some unique continuation results for the normal operator…