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Tensor Voices is a short podcast series about tensors.Themes and summary (AI-generated based on podcaster-provided show and episode descriptions):
➤ tensors for multivariate data encoding • tensor completion, decomposition, networks • algebraic geometry: ranks, secant varieties, apolarity, tensor varieties • numerical issues: condition numbers, interval arithmetic • applications in signal processing, gene expression, PCAThis podcast is a short series focused on tensors and the mathematical ideas and applications that surround them. Across the episodes, the discussions frame tensors as natural representations of multivariate data and as generalizations of matrices, highlighting how moving beyond the matrix setting introduces new geometric, algebraic, and computational phenomena.
A recurring theme is tensor decomposition and rank. The content touches on notions such as symmetric tensors viewed as homogeneous polynomials, Waring rank, apolarity, and secant varieties, along with questions and counterexamples that shape how tensor rank behaves in theory. Related geometric perspectives include rank-one completion problems and the study of tensor network varieties, aiming to describe the structure and dimension of spaces defined by low-complexity tensor representations.
The podcast also emphasizes computational and numerical aspects. Topics include condition numbers, ill-posedness, and the use of interval arithmetic, along with broader questions in algebraic and computational complexity (including limitations of familiar algorithms like Gaussian elimination when generalized). On the applied side, tensor decompositions are connected to data analysis and signal processing, with references to principal component analysis and to scientific data contexts such as multi-tissue gene expression experiments.
Overall, the series presents tensors as a unifying object linking multilinear algebra, algebraic geometry, numerical analysis, and data-driven applications.
| Episodes: |
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Kaie Kubjas 2021-Mar-29 |
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Paul Breiding 2021-Mar-29 |
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Alessandro Oneto 2021-Mar-29 |
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Mateusz Michalek 2021-Mar-29 |
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Anna Seigal 2021-Mar-29 |