BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sebastian Debus (Univ. of Tromsoe\, Norway) DTSTART:20220420T080000Z DTEND:20220420T090000Z DTSTAMP:20260423T035605Z UID:Aromath/2 DESCRIPTION:Title: (Even) Symmetric PSD and SOS forms\nby Sebastian Debus (Univ. of Troms oe\, Norway) as part of Aromath seminar\n\n\nAbstract\nIn this talk we con sider the so-called non-normalized limits of symmetric and even symmetric forms (homogeneous polynomials). To do so\, we identify (even) symmetric f orms of degree d for sufficiently many variables. The sets of positive sem idefinite (non negative) and sums of squares of fixed degree form nested d ecreasing sequences under this identification. We completely characterize the question of non-negativity versus sums of squares in the non-normalize d limit case. We begin by examining the symmetric quartics and provide tes t sets for non negativity and the property of being a sum of squares for t he limit forms\, and give interesting examples. Then\, we consider even sy mmetric sextics and prove that the set of all psd limit forms is not semia lgebraic and provide test sets as well (based on the work of Choi-Lam-Rezn ick). Finally\, we study the tropicalizations of the duals to even symmetr ic psd and sos forms. Tropicalization reduces the study of even symmetric limit cones to the study of polyhedral cones. \nThis is joint work togethe r with Jose Acevedo\, Greg Blekherman and Cordian Riener.\n LOCATION:https://researchseminars.org/talk/Aromath/2/ END:VEVENT END:VCALENDAR