Sharp Estimates for Gowers Norms on Discrete Cubes

Explore sharp estimates for Gowers norms on discrete cubes in this 57-minute lecture by Vjekoslav Kovač from the Hausdorff Center for Mathematics. Delve into optimal dimensionless estimates between Gowers U^k norms and l^p norms for functions supported on the discrete cube [n]^d. Examine sharp inequalities for Gowers-type generalized additive energies for subsets of the same cube, focusing on their size. Discover exact sharp exponents for n=2 and investigate asymptotic estimates as n or k approach infinity. Encounter subtle inequalities for Shannon entropy in the final part of the discussion. Learn about this joint work with Tonći Crmarić from the University of Split, gaining insights into advanced mathematical concepts and their applications in discrete geometry and information theory.