Giorgio Ottaviani (University of Florence)
Tensors can be seen as multidimensional matrices, and are a basic model in data analysis. The world of tensors has both analogies with and differences from the world of classical (bidimensional) matrices. The compelling wish of geometers to think "coordinate-free" gives a different viewpoint on tensor rank, tensor decomposition and spectral theory. In this talk we discuss how algebraic geometry techniques contribute to studying tensors and to extracting useful data from them. For example, one basic question is how to define the determinant of a tensor, while a large amount of recent work concerns the rank and the eigenvectors of tensors and the search for algorithms to compute them.
No familiarity with tensors will be assumed.
Light refreshments will be served before the lecture at 3:30 p.m.