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Texas A&M University

Events for 02/10/2021 from all calendars

Student/Postdoc Working Geometry Seminar

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Time: 10:30AM - 11:30AM

Location: zoom

Speaker: Elina Robeva, UBC

Title: Orthogonal decomposition of tensor trains

Abstract: Tensor decomposition has many applications. However, it is often a hard problem. Orthogonally decomposable tensors form are a small subfamily of tensors and retain many of the nice properties of matrices that general tensors don't. A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. The decomposition of such tensors can be found efficiently, their eigenvectors can be computed efficiently, and the set of orthogonally decomposable tensors of low rank is closed and can be described by a set of quadratic equations. One of the issues with orthogonally decomposable tensors, however, is that they form a very small subset of the set of all tensors. We expand this subset and consider orthogonally decomposable tensor trains. These are formed by placing an orthogonally decomposable tensor at each of the vertices of a tensor train, and then contracting. We give algorithms for decomposing such tensors both in the setting where the tensors at the vertices of the tensor train are symmetric and non-symmetric. This purely theoretical work is based on joint work with Karim Halaseh and Tommi Muller.

Groups and Dynamics Seminar

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Time: 12:00PM - 1:00PM

Location: online

Speaker: Konrad Wrobel, Texas A&M

Title: Cost of inner amenable equivalence relations

Abstract: Cost is a $[1.\infty]$-valued measure-isomorphism invariant of aperiodic measured equivalence relations defined by Gilbert Levitt and heavily studied by Damien Gaboriau. For a large class of equivalence relations, including amenable, the cost is 1. Yoshikata Kida and Robin Tucker-Drob recently defined the notion of an inner amenable equivalence relation as an analog of inner amenability in the setting of groups. We show inner amenable equivalence relations also have cost 1. This is joint work with Robin Tucker-Trob.