BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilya Smirnov (Stockholm University) DTSTART:20210128T210000Z DTEND:20210128T223000Z DTSTAMP:20260423T021424Z UID:FOTR/35 DESCRIPTION:Title: Th e quest for F-rational signature\nby Ilya Smirnov (Stockholm Universit y) as part of Fellowship of the Ring\n\n\nAbstract\nStrongly F-regular sin gularities are one of the fundamental classes of singularities defined by the properties of Frobenius endomorphism. This class of mild singularities can be detected using F-signature\, an invariant of a local ring with man y good properties. Through this connection we obtain a powerful tool for s tudying strongly F-regular singularities\, for example\, several results o n "mildness" of F-regular can be quantified using F-signature. \n\nAnothe r fundamental class of singularities in positive characteristic are F-rati onal singularities. While generally more severe\, this class of singularit ies is in many aspects analogous to strongly F-regular singularities and c an be even understood by "moving" the definition of F-regularity to take p lace in the dualizing module. Naturally\, there has been interest in adapt ing the definition of F-signature to work with F-rational singularities. \ n\nWhile there is no complete solution yet\, I am convinced that such a th eory should exist. As my evidence\, I will present results of a joint work with Kevin Tucker\, and prior works of Hochster and Yao\, and Sannai.\n\n My talk will be self-contained. I will discuss all necessary background\, such as definitions\, properties\, and relations between these notions\, i n the first half and then proceed to more technical results in the second half.\n LOCATION:https://researchseminars.org/talk/FOTR/35/ END:VEVENT END:VCALENDAR