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SUMMARY:Effective results on the size and structure of sumsets - Aled Walk
 er (King's London) 
DTSTART:20220224T143000Z
DTEND:20220224T153000Z
UID:TALK170708@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:Given a finite set A of integer lattice points in d-dimensiona
 l\nspace\, in 1992 Khovanskii proved that the size of the iterated sumset 
 NA is\ngiven exactly by a polynomial P(N) of degree at most d (once N is\n
 sufficiently large). But what does 'sufficiently large' mean in practice?\
 nKhovanskii's original proof was ineffective. Via other methods\,\neffecti
 ve bounds\nhave been proved in a few special cases: when d = 1\, due to Na
 thanson\; when\nthe convex hull of A is a d-simplex\, due to Curran-Goldma
 kher\; and when |A|\n= d + 2\, also due to Curran-Goldmakher. In this talk
  I will discuss joint\nwork with Andrew Granville and George Shakan\, in w
 hich we proved an\neffective bound in the general setting. I will also dis
 cuss our related\nresults on the structure of NA (for large N). 
LOCATION:MR12
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