Site • RSS • Apple PodcastsDescription (podcaster-provided):
Tensor Voices is a short podcast series about tensors.Themes and summary (AI-generated based on podcaster-provided show and episode descriptions):
➤ tensors as multivariate data models • tensor rank, completion, networks • algebraic geometry: secant varieties, apolarity • tensor decompositions for signal processing, genomics • complexity, numerical methods, PCAThis podcast is a short series focused on tensors, emphasizing how they model and analyze multivariate data and how they generalize familiar matrix-based ideas. Across the conversations, tensors are presented both as practical data structures and as objects with rich mathematical geometry.
A recurring theme is tensor decomposition and related notions of rank, including symmetric tensors viewed as homogeneous polynomials. The series touches on topics such as Waring rank, apolarity, secant varieties, and questions about how tensor rank behaves under symmetry assumptions. It also explores tensor completion and rank-one structure, along with the geometry and dimension of tensor network varieties and the complexity of multilinear maps.
Several episodes connect tensor theory to computational concerns: numerical stability, condition numbers, ill-posedness, and the use of interval arithmetic. There is attention to algorithmic and complexity-theoretic perspectives, including the limits of classical procedures like Gaussian elimination when generalized beyond matrices.
Applications and motivations appear throughout, including signal processing, principal component analysis, and multivariate data analysis more broadly. The podcast also points to areas where tensor methods intersect with algebraic geometry, nonlinear algebra, and numerical tensor calculus, framing tensors as central tools for finding structure in complex, high-dimensional datasets.
| Episodes: |
|
Kaie Kubjas 2021-Mar-29 |
|
Paul Breiding 2021-Mar-29 |
|
Alessandro Oneto 2021-Mar-29 |
|
Mateusz Michalek 2021-Mar-29 |
|
Anna Seigal 2021-Mar-29 |