An optimal inverse theorem for tensors over large fields, II

We will give more details about our recent proof, joint with Alex Cohen, showing that the partition rank and the analytic rank of tensors are equal up to a constant, over finite fields of every characteristic and of mildly large size (independent of the number of variables). Proving the equivalence between these two quantities is a central question in additive combinatorics, the main question in the "bias implies low rank" line of work, and corresponds to the first non-trivial case of the Polynomial Gowers Inverse conjecture. The talk will be a continuation of Alex Cohen’s talk from December 2nd, though I will aim for it to be mostly self-contained.

Guy Moshkovitz