A geometric characterization of discrete Guichard nets and their transformations in integrable geometry

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Gudrun worked on the following projects:1) The study of discrete channel surfaces, as joint work with myself and Gudrun's former Ph.D. advisor Udo Hertrich-Jeromin at the Technical University of Vienna. Following clues from the theory of smooth channel surfaces, which can be thought of as tubes with varying radius as one moves along a non-circular direction of the surface, Gudrun established why one particular way of discretizing is the best choice. Gudrun further examined possible applications, finding a characterization of discrete isothermic channel surfaces, and finding connections with multi-circular discrete nets. This work has been submitted for publication.2) The study of discrete Guichard triply orthogonal systems, joint work with Joseph Cho at Kobe University and myself. In particular, Gudrun made the interesting discovery that the conformal diagonal surfaces of Guichard triply orthogonal systems can be minimal surfaces.3) The study of Combescure and Ribaucour transformations of Guichard nets, as an extension of her Ph.D. thesis.4) The study of discrete R-congruences, work that Gudrun is conducting with Thilo Roerig of the Technical University of Berlin.All four projects described above were successful and are of interest to other researchers in Gudrun's field.