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SUMMARY:Mel Nathanson (CUNY)
DTSTART:20200601T133000Z
DTEND:20200601T135500Z
DTSTAMP:20260423T011056Z
UID:CANT2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/2/"
 >Fundamental theorems in additive number theory</a>\nby Mel Nathanson (CUN
 Y) as part of Combinatorial and additive number theory (CANT 2021)\n\n\nAb
 stract\nLet $A$ be a subset of the integers $\\mathbf Z$\, of the lattice 
 ${\\mathbf Z}^n$\, \nor of any additive abelian semigroup $X$.   \nThe cen
 tral problem in additive number theory is to understand the $h$-fold sumse
 t \n\\[\nhA = \\{a_1+\\cdots + a_h : a_i \\in A \\text{ for all } i=1\,\\l
 dots\, h \\}.\n\\]\nIf $A$ is finite\, what is the size of the sumset $hA$
 ?  If $A$ is infinite\, what is the density \nof $hA$?   What is the struc
 ture of the sumset $hA$?   \nDescribe this for small $h$\, and also asympt
 otically as $h \\rightarrow \\infty$.  \nIn how many ways can an element $
 x \\in X$ be represented as the sum of $h$ elements \nof $A$?   For fixed 
 $r$\, what is the subset of $hA$ consisting of elements that have \nat lea
 st $r$ representations? \nClassical problems consider sums of squares\, of
  $k$th powers\, and of primes\, \nbut the general case is also important. 
  \nThis talk will discuss both old and very recent results about sumsets.\
 n
LOCATION:https://researchseminars.org/talk/CANT2020/2/
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