Saarland University
Together with Francesco Galuppi, Kaie Kubjas, Alessandro Oneto, Pierpaola Santarsiero, Luca Sodomaco, Neriman Tokcan, Nick Vannieuwenhoven, we organized two Minisymposia, with four sessions each, on Tensors and related topics at the SIAM AG'2023 conference, at Eindhoven, July 10-14, 2023. The two Minisymposia are:
Just as matrices play a central role in linear algebra, tensors are the main actors of multilinear algebra. From mathematics to computer science, from engineering to physics, the reason for their success is that they provide a natural and compact way to store information. A standard way to extract information from tensors is to consider structured decompositions, with respect to some notion of rank which typically has a natural geometric interpretation. Algebraic geometry provides the right tools to study these structured decompositions.
The Minisymposium focuses on two areas of the study of tensors: the theory of secant varieties and the spectral theory of tensors. The first one is an object of a long line of research, starting from classical work from the XIX and early XX century to state-of-the-art pure and applied mathematics. The second one is a young subject, which has strong connections to optimization and witnessed promising developments in the last few years.
We bring together experts in the field as well as young researchers with the purpose of providing an overview on recent developments in algebraic geometry for the study of tensors. In this way, the minisymposium offers a theoretical perspective which is complementary to the minisymposium “Tensors in Applications”.
The speakers of this Minisymposium are:
With the recent advances in information technology, high-dimensional datasets are commonplace. They exceed the capacity of matrix-based representation of data and linear algebra based analysis approaches. Multilinear algebra and algebraic geometry provide elegant, fundamental tools to study high-dimensional data. Tensors and their decompositions can provide compact and interpretable representation of multimodal data. In applications, it is widely recognized that tensor decomposition can unveil special patterns in data, and determine the fundamental parameters of a specific model. Tensor decomposition methods have been used for various tasks such as dimension reduction, data denoising, data fusion, and missing data completion. They have found applications in several domains including bioinformatics, computer science, physics, social computing, and chemistry. An important goal of the minisymposium is creating bridges between researchers from different mathematically-oriented areas; from algebraic geometry and commutative algebra to quantum information theory, machine learning, and computational biology. For example, some of the presented works relate tensors to phylogenetics, cancer genomics, algebraic statistics, probability theory, graphical models, and quantum physics. This minisymposium offers a more applied perspective, complementary to the minisymposium on “Tensors in Algebraic Geometry,” which focuses on a more algebraic point of view.
The speakers of this Minisymposium are: