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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):
➤ Multivariate data encoding • Tensor network complexity • Symmetric tensors • Rank and decomposition • Algebraic geometry applications • Signal processing • Data structure analysis • Nonlinear algebra"Tensor Voices" is a short podcast series that delves into the world of tensors and their various applications across multiple disciplines. The podcast provides a rich tapestry of discussions led by experts in the field, each episode diving into specific aspects of tensor theory and its practical implications.
A recurring theme throughout the episodes is the fundamental role tensors play in encoding multivariate data, presenting a natural framework for various scientific and mathematical applications. Unlike matrices, which are often viewed as less complex, tensors allow for a broader and deeper exploration of data structures and relationships. The podcast examines how tensors intersect with algebraic geometry, focusing on condition numbers, ill-posed loci, and tensor decompositions, which are crucial for understanding and solving complex algebraic problems.
Applications in signal processing and gene expression experiments highlight tensors as a powerful tool for finding and interpreting structures in data, offering insights into underlying patterns that might otherwise remain hidden. The discussions extend to the geometry and complexity of tensors, with topics such as tensor network complexity, multilinear maps, and tensor decomposition drawing particular attention. The podcast also explores the concept of tensor rank, Waring rank, and secant varieties, shedding light on symmetric and partially symmetric tensors and their relevance in solving higher-dimensional algebraic problems.
Across its episodes, this podcast conveys the ubiquity of tensors, presenting them as indispensable elements in both theoretical and applied research. It articulates the complexities and the potential of tensors to transform our understanding of data and shape the future of various scientific fields, from nonlinear algebra to signal processing and beyond. This podcast caters to those interested in the mathematical intricacies of tensors and their real-world applications.
| 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 |