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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 in multivariate data • Tensor decompositions • Algebraic geometry applications • Symmetric tensors and polynomials • Nonlinear algebra • Data structure analysis • Signal processing • Numerical methods in tensor calculusThis podcast, titled "Tensor Voices," is a series dedicated to exploring tensors, their applications, and the broader mathematical context in which they reside. The show delves into the theoretical and practical aspects of tensors, highlighting their role as a fundamental tool for encoding multivariate data. It presents discussions on the geometric challenges of tensor completion and the complexity associated with tensor network models.
Listeners may expect in-depth examinations of tensors in relation to matrices, exploring how these objects compare and contrast, and discussing tensor decomposition methods that are essential for various scientific experiments and data analysis tasks, particularly in gene expression studies and signal processing. The use of tensor decompositions in practical applications, especially in the field of signal processing, underscores their versatility and importance.
Symmetric tensors are another recurring subject, often analyzed through the lens of polynomial theory. The podcast presents complex mathematical problems like Waring rank and secant varieties, introducing listeners to advanced concepts such as apolarity and symmetrical variants of well-known mathematical problems.
Additionally, the series addresses the ubiquity of tensors in various scientific domains, touching on computational efficiency with techniques like Gaussian elimination and exploring the connections between tensor calculus and algebraic complexity theory. The discussions are enriched by references to notable works and literature in the field, encouraging a deeper dive into topics like numerical tensor calculus and non-linear algebra.
The overarching theme is finding structure in complex data, with tensors frequently employed to uncover insights through methods such as principal component analysis. This podcast offers a comprehensive overview of the role tensors play in contemporary mathematical research and application, providing valuable insights into their theoretical underpinnings and real-world implications.
| 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 |