BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Akshat Mudgal (University of Oxford) DTSTART:20230118T160000Z DTEND:20230118T170000Z DTSTAMP:20260418T064344Z UID:LNTS/87 DESCRIPTION:Title: Ad ditive equations over lattice points on spheres\nby Akshat Mudgal (Uni versity of Oxford) as part of London number theory seminar\n\nLecture held in Rm. 706\, UCL Department of Mathematics (UCL Union Building).\n\nAbstr act\nIn this talk\, we will consider additive properties of lattice points on spheres. Thus\, defining $S_m$ to be the set of lattice points on the sphere $x^2 + y^2 + z^2 + w^2 = m$\, we are interested in counting the num ber of solutions to the equation\n$$a_1 + a_2 = a_3 + a_4\,$$\nwhere $a_1\ ,\\dots\, a_4$ lie in some arbitrary subset $A$ of $S_m$. Such an inquiry is closely related to various problems in harmonic analysis and analytic n umber theory\, including Bourgain's discrete restriction conjecture for sp heres. We will survey some recent results in this direction\, as well as d escribe some of the various techniques\, arising from areas such as incide nce geometry\, analytic number theory and arithmetic combinatorics\, that have been employed to tackle this type of problem.\n LOCATION:https://researchseminars.org/talk/LNTS/87/ END:VEVENT END:VCALENDAR