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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 and geometry • tensor rank, Waring rank, apolarity, secant varieties • tensor completion, decompositions, tensor networks • condition numbers, ill-posedness, interval arithmetic • applications in multivariate data, gene expression, signal processing, PCA • algebraic complexityThis podcast is a short series focused on tensors and their role in modern mathematics and data analysis. Across conversations with researchers, it treats tensors as higher-dimensional generalizations of matrices and as a natural language for representing multivariate structure. A recurring theme is tensor rank and tensor decomposition: how to express complex multiway data as sums of simpler components, how to compute or approximate such decompositions, and what makes these problems difficult in theory and practice.
Much of the content draws on algebraic geometry and related “nonlinear algebra” perspectives, connecting tensors to objects such as secant varieties, rank-one varieties, and tensor network varieties. Symmetric tensors are discussed through their identification with homogeneous polynomials, bringing in topics like Waring rank and apolarity and illustrating how classical polynomial questions map to tensor problems. The series also addresses numerical and computational aspects, including condition numbers, ill-posedness, and the practical challenges that distinguish tensor problems from familiar linear-algebraic ones.
Applications appear as well, framing tensors as tools for extracting structure from data. Topics include multivariate data encoding, principal component analysis in a tensor setting, signal processing uses of tensor decompositions, and examples from scientific data such as multi-tissue gene expression experiments. Overall, the podcast emphasizes both the theoretical foundations and the computational and applied motivations that make tensors central across geometry, complexity theory, and data-driven fields.
| 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 |