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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 representation •rank, decomposition, completion •tensor networks and complexity •algebraic geometry: secant varieties, apolarity, condition numbers •applications in gene expression, signal processing, PCAThis podcast is a short series of conversations focused on tensors and the mathematical and computational ideas that surround them. Across the episodes, tensors are presented as natural representations of multivariate data and as a unifying object that generalizes familiar matrix-based concepts. The discussions connect tensors to geometry and algebra, including viewpoints that treat symmetric tensors as homogeneous polynomials and explore topics such as rank (including Waring rank), apolarity, secant varieties, and related open problems and counterexamples.
A recurring theme is tensor decomposition and completion: how higher-order data can be factored into structured components, what makes these problems difficult, and how notions like condition numbers and ill-posedness affect computation. The podcast also touches on tensor networks and tensor network varieties, highlighting complexity questions for multilinear maps and structured representations.
Applications and motivation come from data analysis and scientific computing, with examples spanning signal processing, principal component analysis, and multilevel or multi-tissue gene expression experiments. Alongside applications, the series points to algorithmic and complexity-theoretic perspectives, including limits of classical procedures like Gaussian elimination when generalized beyond matrices, and references to nonlinear algebra, numerical tensor calculus, and interval arithmetic as tools for reliable computation.
Overall, the content emphasizes how tensors link algebraic geometry, numerical analysis, complexity theory, and data-driven applications, and how structural properties of tensors influence both theory and computation.
| 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 |