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 Cohenâ€™s talk from December 2nd, though I will aim for it to be mostly self-contained.

Guy Moshkovitz