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Overview
Tensors are the higher-dimensional generalization of matrices, and as such provide a natural and useful way of organizing data. Viewing tensors as geometric objects gives us powerful methods to extract information from this data, and is also a beautiful subject in its own right.
The first part of this seminar is an introduction to tensors and tensor decomposition, where we will learn and apply techniques from multilinear algebra, algebraic geometry, and representation theory. In the second part we will discuss some applications, depending on the interests of the participants. Possible topics include the complexity of matrix multiplication, tensor networks in quantum mechanics, and algebraic versions of P vs NP.
Our main resource will be the book Tensors: geometry and applications by Joseph M. Landsberg. (See here for a list of errata.)
Schedule
The seminar will take place on Tuesdays, 16:00-18:00, at KU Leuven campus Arenberg 3, in the seminar rooms B00.18 (full name 200B.00.018; ground floor of the Math building 200B) and S00.04 (full name 200B.00.018; ground floor of the seminar building 200S).
February 1, 2023 (Wednesday): Tim Seynnaeve -- Introduction
February 14, 2023, B00.18: Tim Seynnaeve -- Multilinear algebra
February 21, 2023, B00.18: Francesca Zaffalon -- Algebraic geometry for spaces of tensors -- Notes
February 28, 2023, S00.04: Daniele Taufer -- Secant varieties
March 7, 2023, S00.04: Giacomo Masiero -- Representation theory, part 1
March 14, 2023, S00.04: Sebastian Seemann -- Representation theory, part 2
March 21, 2023, B00.18: Riccardo Invernizzi -- Representation theory, part 3
March 28, 2023, B00.18: Erdenebayar Bayarmagnai -- Equations for secant varieties, part 1
April 18, 2023, B01.18, Exceptionally 10:00-12:00: Nick Vannieuwenhoven -- Tensor decomposition -- Slides
April 25, 2023, S00.04: Sebastian Seemann -- Equations for secant varieties, part 2
May 2, 2023, B00.05: Tim Seynnaeve -- Equations for secant varieties, part 3
May 9, 2023, S00.04: Simon Jacobsson -- Normal forms for small tensors
May 16, 2023, S00.04: Tim Seynnaeve -- Fast Matrix Multiplication
May 23, 2023, S00.04: Daniele Taufer -- Symmetric tensor rank
Organizers
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