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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):
➤ tensor theory for multivariate data • tensor decompositions, completion, PCA • tensor networks, varieties, algebraic geometry • symmetric tensors, Waring rank, apolarity • numerical methods, condition numbers, interval arithmetic • applications in signal processing, gene expressionThis podcast is a short series focused on tensors and the mathematics and computation surrounding them, often through conversations centered on individual researchers’ perspectives. Across the episodes, tensors are presented as a natural language for multivariate data and as a generalization beyond matrices, with attention to why tensor problems behave differently and can be more subtle.
Common themes include tensor decomposition and notions of tensor rank, including structured settings such as symmetric and partially symmetric tensors, and connections to homogeneous polynomials. The discussions touch on geometric and algebraic viewpoints—such as secant varieties, apolarity, and tensor network varieties—used to understand identifiability, dimension, and complexity of tensor models. There is also emphasis on computational aspects: condition numbers, ill-posedness, and numerical concerns (including interval arithmetic) that affect practical tensor computations.
Several threads connect tensor methods to applications and data analysis. Topics include rank-one tensor completion, tensor network complexity of multilinear maps, and approaches for extracting structure from data, with links to techniques analogous to principal component analysis. Application areas mentioned include signal processing and biological data analysis, such as decompositions for multi-tissue gene expression experiments.
Overall, the content sits at the intersection of multilinear algebra, algebraic geometry, numerical analysis, and complexity theory, aiming to clarify how tensors are modeled, decomposed, and analyzed in both theoretical and applied settings.
| 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 |