Gowers-Host-Kra Norms and Gowers Structures on Euclidean Spaces
The investigation on Brascamp-Lieb data — their structure, their extremizability, their stability and regularity of their constants — has been an active parat of Harmonic Analysis. In this talk, I’ll present an example of a Brascamp-Lieb structure: a so-called Gowers structure on Euclidean spaces, together with the related Gowers-Host-Kra norms. These were originally tools used in additive combinatorics. I’ll discuss what happens when a function nearly achieves its Gowers-Host-Kra norm in a Euclidean context — this can be seen as continuation of the work of Eisner and Tao — and a related stability result of the Gowers structure on Euclidean spaces.