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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 encoding multivariate data • tensor decomposition/completion • rank, Waring rank, apolarity, secant varieties • tensor networks and complexity • condition numbers, ill-posedness, interval arithmetic • applications in gene expression, signal processing, PCAThis podcast is a short series focused on tensors, emphasizing both their mathematical foundations and their role as a language for representing multivariate data. Across the conversations, tensors are presented as a generalization beyond matrices, with attention to why higher-order structure changes both theory and computation. A recurring theme is tensor rank and tensor decomposition: how to express complicated data or multilinear maps as combinations of simpler components, how different notions of rank arise (including symmetric and partially symmetric settings), and what is known—and not known—about uniqueness, identifiability, and limits of existing conjectures.
The series also highlights geometric and algebraic viewpoints. Topics include the geometry of low-rank and rank-one models, secant varieties and apolarity methods connected to Waring-type decompositions, and tensor network varieties that describe structured low-complexity representations. Alongside these are numerical and algorithmic concerns: the conditioning of tensor problems, loci where problems become ill-posed, and the use of tools like interval arithmetic to reason about reliability of computations. There is also discussion of complexity-theoretic perspectives on multilinear computation, including when familiar linear-algebraic procedures do not extend optimally to the tensor setting.
Applications serve as motivation and context, particularly in data analysis and the sciences. The podcast connects tensor methods to signal processing, principal component analysis–style objectives, and biological data such as multi-tissue gene expression experiments, framing tensors as a way to “find structure in data” by exploiting multiway relationships. Overall, listeners can expect a research-oriented tour through tensor decomposition, geometry, numerical stability, and applications where multi-dimensional data representations are central.
| 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 |