BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Satoshi Murai (Waseda University) DTSTART:20210325T220000Z DTEND:20210325T233000Z DTSTAMP:20260423T035915Z UID:FOTR/39 DESCRIPTION:Title: Be tti numbers of monomial ideals fixed by permutations of the variables\ nby Satoshi Murai (Waseda University) as part of Fellowship of the Ring\n\ n\nAbstract\nLet R_n be the polynomial ring with n variables over a field K. We consider the natural action of the n-th symmetric group S_n to R_n. In this talk\, I will mainly talk about the following problem: Fix monomia ls u_1\,\\dots\,u_m and consider the ideal I_n of R_n generated by the S_n -orbits of these monomials. How the Betti numbers of I_n change when n inc reases?\nI will explain that there is a simple way to determine non-zero p ositions of the Betti table of I_n when n is sufficiently large. I also ex plain that we can determine the Betti numbers of I_n by considering the S_ n-module structure of Tor_i(I_n\,K).\n\nThe above problem is motivated by recent studies of algebraic properties of S_n-invariant ideals and is insp ired by studies of Noetherianity up to symmetry. I will explain this motiv ation and basic combinatorial properties of S_n-invariant ideals in the fi rst part of the talk.\nThis talk includes a joint work with Claudiu Raicu. \n LOCATION:https://researchseminars.org/talk/FOTR/39/ END:VEVENT END:VCALENDAR