DMS Colloquium: Emanuele Ventura

Speaker: Emanuele Ventura, Postdoc Texas A&M; Ph.D., Aalto University (Helsinki, Finland) 2017

Title: Tensors and their symmetry groups

Abstract: Tensors (multi-dimensional matrices) appear in many areas of pure and applied mathematics. I will discuss their use in algebraic complexity theory. Matrix multiplication is a tensor and its complexity is encoded in its tensor rank. To analyze the complexity of the matrix multiplication tensor, Strassen introduced a class of tensors that vastly generalize it, the tight tensors. These tensors have continuous symmetries. Pushing Strassen’s ideas forward, with A. Conner, F. Gesmundo, and J.M. Landsberg, we investigate tensors with large symmetry groups and classify them under a natural genericity assumption. Our study provides new paths towards upper bounds on the complexity of matrix multiplication.