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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 and multivariate data representation • tensor decomposition, ranks, tensor networks • algebraic geometry: secant varieties, apolarity, completion • numerical conditioning, complexity theory • 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 a natural language for multivariate data and as higher-order generalizations of matrices, while also emphasizing that tensors behave differently from matrices in ways that matter for computation, geometry, and modeling.
A recurring theme is tensor decomposition and rank: how tensors can be represented as sums of simpler components, how rank is defined in different settings (including symmetric and partially symmetric cases), and how rank relates to classical topics such as homogeneous polynomials, Waring rank, apolarity, and secant varieties. Alongside these conceptual questions, the podcast touches on when tensor problems become ill-conditioned or ill-posed, and why numerical considerations—such as condition numbers and interval arithmetic—are important when working with tensor data and algorithms.
The series also highlights connections to algebraic geometry and nonlinear algebra, using geometric viewpoints to study objects like rank-one tensor completion, tensor network varieties, and the complexity of multilinear maps. Computational complexity appears as another thread, including the limitations of familiar linear-algebraic tools (for example, analogies to Gaussian elimination) when extended to tensor settings.
Applications and data-analytic motivations surface throughout, including how tensor methods help uncover structure in data, links to principal component analysis, and examples from areas such as signal processing and multi-tissue gene expression experiments. Overall, the podcast presents tensors as a unifying object bridging abstract theory, algorithmic challenges, and practical uses in modern data-driven contexts.
| 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 |