BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jonathan Campbell (Center for Communications Research La Jolla) DTSTART:20201005T203000Z DTEND:20201005T213000Z DTSTAMP:20260423T004916Z UID:MITTop/14 DESCRIPTION:Title: Homotopy Theory and Hilbert's Third Problem\nby Jonathan Campbell (Cen ter for Communications Research La Jolla) as part of MIT topology seminar\ n\n\nAbstract\nIn this talk I'll explain how one might attack Hilbert's Ge neralized Third\nProblem via homotopy theory\, and describe recent progres s in this direction. Two\nn-dimensional polytopes\, $P$\, $Q$ are said to be scissors congruent if one can\ncut $P$ along a finite number of hyperpl anes\, and re-assemble the pieces into\n$Q$. The scissors congruence probl em\, aka Hilbert's Generalized Third Problem\,\nasks: when can we do this? What obstructs this? In two dimensions\, two polygons\nare scissors congr uent if and only if they have the same area. In three\ndimensions\, there is volume and another invariant\, the Dehn Invariant. In higher\ndimension s\, very little is known --- but the problem is known to have deep\nconnec tions to motives\, values of zeta functions\, the weight filtration in\nal gebraic K-theory\, and regulator maps. I'll give a leisurely introduction to\nthis very classical problem\, and explain some new results obtained vi a homotopy\ntheoretic techniques. This is all joint with Inna Zakharevich .\n\n\n\nAdd this seminar to your calendar : http://math.mit.edu/topology/ topology_seminar.ics\n LOCATION:https://researchseminars.org/talk/MITTop/14/ END:VEVENT END:VCALENDAR