BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georgios Kotsovolis (Princeton University) DTSTART:20241205T130000Z DTEND:20241205T140000Z DTSTAMP:20260423T021333Z UID:GANT/67 DESCRIPTION:Title: Ba ss Note Spectra of Binary Forms\nby Georgios Kotsovolis (Princeton Uni versity) as part of Greek Algebra & Number Theory Seminar\n\n\nAbstract\nF or some homogeneous polynomial $P$ in $k$ variables and some unimodular $k $-dimensional lattice $\\Lambda$\, what is the smallest value that $\\vert P\\vert$ assumes on the non-zero vectors of $\\Lambda$? The set we obtain by varying $\\Lambda$ in the moduli space of unimodular lattices\, is ref erred to as the bass note spectrum of $P$. While this set is fundamental i n the geometry of numbers\, not many cases are understood. Even in dimensi on 2\, the problem has been solved only when $P$ is $\\mathbb{R}$-anisotro pic or a quadratic form. In this talk\, we will explain Mordell's and Dave nport's theorems on the spectra of binary cubic forms and further explain how to resolve this problem for all binary forms of any degree.\n LOCATION:https://researchseminars.org/talk/GANT/67/ END:VEVENT END:VCALENDAR