BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joachim Jelisiejew (University of Warsaw) DTSTART:20220930T120000Z DTEND:20220930T130000Z DTSTAMP:20260423T021051Z UID:VCAS/140 DESCRIPTION:Title: W hen is a homogeneous ideal a limit of saturated ones?\nby Joachim Jeli siejew (University of Warsaw) as part of IIT Bombay Virtual Commutative Al gebra Seminar\n\n\nAbstract\nLet I be a homogeneous ideal in a polynomial ring S. If the Hilbert function of S/I is admissible\, for example (1\,n\, n\,n\,...) is it natural to ask whether I is a limit of homogeneous ideals : does there exist a ideal F in S[t] such that F(t = 0) is equal to I\, wh ile F(t = lambda) is a saturated homogeneous ideal for lambda general. Exa mples of such limits (for the above Hilbert function) can be constructed e .g. by degenerating I(Gamma)\, where Gamma is a tuple of n general points on the projective space associated to S. However\, to decide whether a giv en ideal I is a limit is very much nontrivial. This problem very recently became of key interest for applications in the theory of tensors: proving that certain ideals are not limits would improve best known lower bounds o n border ranks of certain important tensors.\nIn the talk I will report ho w surprisingly little is known and present some recent results and some ch allenges\, both theoretical and computational. All this is a joint work w ith Tomasz Mandziuk.\n LOCATION:https://researchseminars.org/talk/VCAS/140/ END:VEVENT END:VCALENDAR