Foundational Tensor Theory Reading Group, Fall 2016

Mondays, 12pm-1pm. Evans Hall, Room 891

Organizers: Anna Seigal and Rocky Foster

Based on the book "Tensor Spaces and Numerical Tensor Calculus" by Wolfgang Hackbusch.

In this semester's version of the seminar, we are studying the third part of the book, which primarily deals with representing and approximating tensors, and applications. Talks will be given on r-term representation, tensor subspace representation, a hybrid form between the two, as well as other topics according to the interests of the speaker. Please don't hesitate to join us: all are welcome.


August 29th: Organizational Meeting

September 6th: Eric Hallman, Matrix Tools. Suggested reading: Chapter 2

September 12th: Noble Macfarlane, Algebraic Foundations of Tensor Spaces. Suggested reading: 1.1-1.4, 3.1-3.2.

September 19th: Onyebuchi Ekenta, Tensors as Matrix Operations. Suggested reading: Section

September 26th Qiaochu Yuan, r-Term Representation. Suggested reading: Sections 7.1.3 and 7.3.

October 3rd: Rocky Foster, Tensor Subspace Representation. Suggested Reading: 8.1-8.3.

October 10th: Alex Rusciano, Hierarchical Tensor Decomposition. Suggested reading: 11.1.

October 17th: Bill Huggins, Tensor Networks in Physics and Chemistry.

October 24th: Dan Erdmann-Pham, Norm Inequalities between Tensor Unfoldings.

October 31st: Anna Seigal, Real Rank Two Geometry.

November 7th: Noble Macfarlane, r-Term Approximation. Suggested Reading: 9.1-9.3.

November 14th: Nikhil Strivastava, Area Laws for 1D Gapped Local Hamiltonians. Abstract: It has been observed for several decades by physicists that the low energy states of "low-dimensional" n-body quantum systems exhibit low entanglement --- i.e., they are in a certain sense well-approximated by tensors of low rank. Over the last few years this has been proven rigorously in the case of one dimensional lattices. We will survey some of the main techniques and results in this area (mainly following the papers of Arad, Landau, Vazirani, and Vidick).

November 21st: Rocky Foster, Use of Tensor Formats in Elliptic Eigenvalue Problems. Based on the paper by Hackbusch, Khoromskij, Sauter, Tyrtyshnikov.

November 28th: Joonho Lee, Cancelled.

December 5th: Anna Seigal, Semi-algebraic geometry of higher order singular values.