BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nil Şahin (Bilkent University) DTSTART:20260219T124000Z DTEND:20260219T133000Z DTSTAMP:20260414T101628Z UID:METU_Math/1 DESCRIPTION:Title: Numerical Semigroups: From the Frobenius Coin Problem to Hilbert Functio ns\nby Nil Şahin (Bilkent University) as part of METU Mathematics Gen eral Seminar\n\nLecture held in Gündüz İkeda Seminar Room\, Mathematics Department.\n\nAbstract\nThe study of numerical semigroups finds its clas sical roots in the "Frobenius Coin Problem"\, famously popularized by J.J. Sylvester in the late 19th century. Sylvester’s initial question "deter mining the largest integer that cannot be expressed as a non-negative inte ger linear combination of a given set of coprime integers" laid the ground work for what is now a rich intersection of combinatorics and commutative algebra.\n\nThrough the construction of semigroup rings\, these combinator ial objects provide a natural framework for studying the geometric and alg ebraic properties of monomial curves. In particular\, the link between the numerical semigroup and the Hilbert function of its associated graded rin g has become a focal point of recent research. Characterizing numerical fu nctions that might be Hilbert functions of one-dimensional Cohen-Macaulay local rings is an open question.\n\nThere is a conjecture by Judith Sally stating that the "Hilbert function of a one-dimensional Cohen-Macaulay loc al ring with small enough embedding dimension is non-decreasing". In this talk\, we will focus on 4-generated symmetric and pseudo-symmetric monomia l curves. We will demonstrate that 4-generated pseudo-symmetric monomial c urves satisfy Sally’s conjecture.\n LOCATION:https://researchseminars.org/talk/METU_Math/1/ END:VEVENT END:VCALENDAR