<!DOCTYPE html><html><body>Achtung:<br> - andere Uhrzeit<br><br><br>E I N L A D U N G<hr>zum Forschungsseminar 'Computergrafik, Bildverarbeitung und Visualisierung'<br><br> am Mittwoch, den 6. Juli 2022, 14:00 Uhr,<br> im Raum P-701 im Paulinum am Augustusplatz, sowie über eine Webkonferenz.<br> (<a href="https://conf.fmi.uni-leipzig.de/b/van-bwb-jil-vk2">https://conf.fmi.uni-leipzig.de/b/van-bwb-jil-vk2</a>)<hr>Wir hören einen Vortrag von<br><br> Prof. Eckhard Hitzer<br><br>mit dem Titel:<br><br> '144 years after Clifford’s “Applications of Grassmann’s Extensive Algebra”'<br><br>zum Inhalt:<br><br> We look at the consequences of Clifford's 1878 landmark paper on<br> “Applications of Grassmann’s Extensive Algebra”. One is certainly the<br> expansion of Jean Baptiste Joseph Fourier's transforms to quaternion and<br> Clifford algebras. A brief introduction to Clifford's geometric algebras<br> will also be given. We look at how meaningful Clifford Fourier transforms<br> can be designed, regarding a Mellin type variant and kernels that capture<br> phase space transformations. Hamilton, Grassmann and Clifford assumed<br> associativity, Cayley and Graves with the octonion algebra abandoned it,<br> creating the highest dimensional known normed division algebra of eight<br> dimensions. Recently a dimensionally minimal embedding of octonion<br> multiplication in Clifford algebra has been found and waits to be further<br> explored and applied. We also introduce application survey literature,<br> with a particular example on airborne laserscanning. For computer science,<br> graphics and robotics (a.o.) socalled conformal geometric algebra (CGA)<br> has proved very versatile. Applying CGA to crystallography closes an<br> interesting circle of mathematical developments that began 200 years ago<br> with Justus G. Grassmann, Hermann's father, and on the way has lead to<br> our current standard notion of vector spaces. As science always progresses,<br> recently expansions of CGA that include conics and quadrics, Darboux<br> Cyclides, and cubic curves and surfaces come under investigation, complete<br> with computational tools (computer algebra and algorithm optimization).<br> PR and conference invitations form a sort of conclusion.<hr>Alle Interessierten sind im Namen von Professor Dr. Scheuermann herzlich<br>eingeladen.<br><br>Mit freundlichen Grüßen<br>Vanessa Kretzschmar</body></html>