BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Prof. Karen E. Smith (University of Michigan) DTSTART:20210408T130000Z DTEND:20210408T150000Z DTSTAMP:20260423T021403Z UID:tmc-dls/11 DESCRIPTION:Title: Extremal singularities in prime characteristic\nby Prof. Karen E. Smi th (University of Michigan) as part of TMC Distinguished Lecture Series\n\ n\nAbstract\nWhat is the most singular possible singularity? What can we s ay about its geometric and algebraic properties? This seemingly naive ques tion has a sensible answer in characteristic p. The "F-pure threshold\," w hich is an analog of the log canonical threshold\, can be used to "measure " how bad a singularity is. The F-pure threshold is a numerical invariant of a point on (say) a hypersurface---a positive rational number that is 1 at any smooth point (or more generally\, any F-pure point) but less than o ne in general\, with "more singular" points having smaller F-pure threshol ds. We explain a recently proved lower bound on the F-pure threshold in te rms of the multiplicity of the singularity. We also show that there is a n ice class of hypersurfaces---which we call "Extremal hypersurfaces"---for which this bound is achieved. These have very nice (extreme!) geometric pr operties. For example\, the affine cone over a non Frobenius split cubic s urface of characteristic two is one example of an "extremal singularity". Geometrically\, these are the only cubic surfaces with the property that * every* triple of coplanar lines on the surface meets in a single point (ra ther than a "triangle" as expected)---a very extreme property indeed.\n\nP rof. Karen E. Smith will deliver a live talk on April 08\, 2021 at 18:30 I ndian time. This talk will be followed by a live interactive session with the speaker.\n LOCATION:https://researchseminars.org/talk/tmc-dls/11/ END:VEVENT END:VCALENDAR