Host-Kra norms and Gowers structure on Euclidean spaces

Series: 
Analysis Seminar
Wednesday, January 24, 2018 - 1:55pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
UC Berkeley
,  
Organizer: 
The investigation on Brascamp-Lieb data - their structure, their extremizability, their stability and regularity of their constants - has been an active one in 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 in additive combinatorics context. I'll dissertate on 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-Tao - and a related stability result of the Gowers structure on Euclidean spaces.