BARC talk by Harold Nieuwboer

Tuesday, April 8, 2025, Harold Nieuwboer, Postdoc with QMATH at the University of Copenhagen, will give a talk on "Computing moment polytopes of tensors, with applications to algebraic complexity theory and quantum information". 

Abstract:
Tensors play a central role in various areas of computer science and mathematics, such as algebraic complexity theory (matrix multiplication), quantum information theory (entanglement), and additive combinatorics (slice rank).
Fundamental problems about tensors are strongly tied to well-known questions in computational complexity --- such as the problem of determining the matrix multiplication exponent via asymptotic rank, and the stronger Strassen asymptotic rank conjecture, which has recently been intimately linked to a whole range of computational problems. The moment polytope of a tensor is a mathematical object that contains "rank"-like information, but little was known about them. We give new practical algorithms for computing them, vastly extending the set of known examples. We also extend our algorithmic observations to show separations between polytopes of matrix multiplication and unit tensors, and we resolve the "hay-in-a-haystack" problem for non-free tensors.

Bio:
Harold Nieuwboer is a postdoctoral researcher at QMATH at the University of Copenhagen, advised by prof. dr. Matthias Christandl and dr. Laura Mančinska. He received his PhD from the University of Amsterdam, where he was advised by prof. dr. Michael Walter and prof. dr. Eric Opdam. He is interested in connections between pure mathematics, quantum physics and theoretical computer science, with an an algorithmic view towards problems from algebra, geometry and quantum information.

Host:
Théo Fabris