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SUMMARY:Steve Senger (Missouri State University)
DTSTART:20200601T200000Z
DTEND:20200601T202500Z
DTSTAMP:20260423T011224Z
UID:CANT2020/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/13/
 ">Point configurations determined by dot products</a>\nby Steve Senger (Mi
 ssouri State University) as part of Combinatorial and additive number theo
 ry (CANT 2021)\n\n\nAbstract\nErdős' unit distance problem has perplexed 
 mathematicians for decades. \nIt asks for upper bounds on how often a fixe
 d distance can occur in a large finite point set in the plane. \nWe offer 
 novel bounds on a family of variants of this problem involving multiple po
 ints\, \nand relationships determined by dot products. Specifically\, give
 n a large finite set $E$ of points \nin the plane\, and a $(m \\times m)$ 
 matrix $M$ of real numbers\, we offer bounds on the number \nof $m$-tuples
  of points from $E$\, $(x_1\, x_2\, \\dots\, x_m)\,$ satisfying $x_i \\cdo
 t x_j = m_{ij}\,$ \nthe $(i\,j)$th entry of $M$.\n
LOCATION:https://researchseminars.org/talk/CANT2020/13/
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