BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kirsten Wickelgren (Duke University) DTSTART:20200601T140000Z DTEND:20200601T150000Z DTSTAMP:20260423T035753Z UID:OATS/7 DESCRIPTION:Title: The re are 160\,839<1> + 160\,650<-1> 3-planes in a 7-dimensional cubic hypers urface\nby Kirsten Wickelgren (Duke University) as part of Online alge braic topology seminar\n\n\nAbstract\nThe expression in the title is a bil inear form and it comes from an Euler number in A1-algebraic topology. Suc h Euler numbers can be constructed with Hochschild homology\, self-duality of Koszul complexes\, pushforwards in SL_c oriented cohomology theories\, and sums of local degrees. We show an integrality result for A1-Euler num bers and apply this to the enumeration of d-planes in complete intersectio ns. Classically such counts are valid over C and sometimes extended to the real numbers\, but A1-homotopy theory allows one to perform counts over a large class of fields\, and records information about the solutions in bi linear form. The example in the title then follows from work of Finashin-- Kharlamov. This is joint work with Tom Bachmann.\n LOCATION:https://researchseminars.org/talk/OATS/7/ END:VEVENT END:VCALENDAR