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SUMMARY:Akshat Mudgal (University of Oxford)
DTSTART:20220603T103000Z
DTEND:20220603T113000Z
DTSTAMP:20260423T022141Z
UID:ntsea/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ntsea/15/">A
 dditive equations over lattice points on spheres</a>\nby Akshat Mudgal (Un
 iversity of Oxford) as part of Number theory by the sea\n\n\nAbstract\nIn 
 this talk\, we will consider additive properties of lattice points on\nsph
 eres. Thus\, defining $S_m$ to be the set of lattice points on the sphere 
 $x^2 + y^2\n+ z^2 + w^2 = m$\, we are interested in counting the number of
  solutions to the\nequation $a_1 + a_2 = a_3 + a_4\,$ where $a_1\, ...\, a
 _4$ lie in some arbitrary subset $A$ of $S_m$. Such an inquiry is closely 
 related to various problems in harmonic analysis and analytic number theor
 y\, including Bourgain's discrete restriction conjecture for spheres. We w
 ill survey some recent results in this direction\, as well as describe som
 e of the various\ntechniques\, arising from areas such as incidence geomet
 ry\, analytic number theory\nand arithmetic combinatorics\, that have been
  employed to tackle this type of\nproblem.\n
LOCATION:https://researchseminars.org/talk/ntsea/15/
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