Incidence theory and restriction estimates
  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 Szemer\'edi-Trotter Theorem. The combination of the two approaches recovers the best known Strichartz estimates for the classical torus in dimensions $n\ge 3$, without any appeal to number theory. 
Ciprian Demeter
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