FB 6 Mathematik/Informatik/Physik

Institut für Mathematik

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Geometry of tensor decompositions




Over the last 60 years tensors and multilinear algebra made their way to the applied sciences and the problem of tensor rank decomposition acquired an increasingly central role. One of the main advantages of working with tensors instead of matrices is that tensors very often admit a unique rank decomposition. Under this perspective, after translating applied problems of different fields in the language of tensors, the uniqueness of the tensor rank decomposition represents a unique way of interpreting latent variables.

In this seminar we will start with a series of lectures, where we will first introduce tensors and explore different notions of rank as well as different notions of symmetries related to tensors. Then, we will study such concepts from a geometric point of view, introducing classical algebraic varieties related to tensors. Lastly, we will focus on the identifiability problem from a pure geometric point of view and we derive standard results on identifiability of tensors that can be useful in different contexts of applied sciences.

Regular attendence of students is expected. Active participation and written work are encouraged. This is a research-oriented course.

Weitere Angaben

Ort: 69/117
Zeiten: Mi. 14:00 - 16:00 (wöchentlich)
Erster Termin: Mittwoch, 12.04.2023 14:00 - 16:00, Ort: 69/117
Veranstaltungsart: Seminar (Offizielle Lehrveranstaltungen)


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