2014/01/09 by Demeter, Ciprian
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1401.1873
We investigate the interplay between the discrete restriction phenomenon and incidence theory. Two angles are explored. One is a refinement of the machinery developed by Thomas Wolff, which when combined with a recent subcritical estimate of Bourgain leads to new Strichartz estimates for irrational tori. The other one connects various additive energies with the Szemerédi-Trotter Theorem. The combination of the two approaches recovers the best known Strichartz estimates for the classical torus in dimensions n≥ 3, without any appeal to number theory.