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SUMMARY:Jacob Denson (Madison)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260423T005705Z
UID:OARS/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/40/">La
 rge Sets with Fourier Decay avoiding Patterns</a>\nby Jacob Denson (Madiso
 n) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe disc
 uss the construction of sets with large Fourier dimension avoiding certain
  families of linear and non-linear patterns. In other words\, we construct
  sets which do not contain a certain subset of points arranged in a partic
 ular configuration\, while also supporting probability measures whose Four
 ier transforms exhibit polynomial decay. Our analysis involves a discussio
 n of the concentration of measure phenomenon in probability\, and some osc
 illatory integral estimates. As particular applications of these methods\,
  we will construct large sets of $\\mathbf{T}^d$ not containing points $x_
 1\,\\dots\,x_n$ solving linear equations of the form $a_1x_1 + ... a_n x_n
  = b$\, and large subsets of planar curves with non-vanishing curvature wh
 ich do not contain three points forming an isosceles triangle.\n
LOCATION:https://researchseminars.org/talk/OARS/40/
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