I will introduce tensors and tensor rank from an algebraic perspective. I will introduce multilinear rank and tensor rank, and I will discuss the related classical algebraic varieties — subspace varieties and secant varieties. I will give basic tools for computing dimensions, Terracini's lemma and the notion of the abstract secant variety. This will lead to the notion of generic rank. I will briefly disucss implicit equations, which lead to rank tests.

The second session of this talk will take place on Friday, September 5 from 9:00 am – 10:00 am.