BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kriti Goel (University of Utah) DTSTART:20221107T210000Z DTEND:20221107T223000Z DTSTAMP:20260423T021323Z UID:FOTR/60 DESCRIPTION:Title: Hi lbert-Kunz function and Hilbert-Kunz multiplicity of ideals and Rees algeb ras\nby Kriti Goel (University of Utah) as part of Fellowship of the R ing\n\n\nAbstract\nHilbert-Kunz functions were introduced by E. Kunz in 19 69 in his work characterizing regular local rings in the prime characteris tic setting. The existence of Hilbert-Kunz multiplicity was proved later b y P. Monsky in 1983. Since then\, Hilbert-Kunz functions and Hilbert-Kunz multiplicities have been extensively studied\, partly because of their con nections with the theory of tight closure and their unpredictable behaviou r. Unlike the Hilbert-Samuel function\, the Hilbert-Kunz function need not be a polynomial function.\n\nIn this talk\, we consider the Hilbert-Kunz function of Rees algebra of ideals and show that\, in certain cases\, it b ehaves as a quasi-polynomial\, a piece-wise polynomial\, or even a polynom ial. We also consider Hilbert-Kunz multiplicity of powers of an ideal\, in an attempt to write it as a function of the power of the ideal. This invo lves a surprising connection with the Hilbert-Samuel coefficients of Frobe nius powers of an ideal.\n LOCATION:https://researchseminars.org/talk/FOTR/60/ END:VEVENT END:VCALENDAR