BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Apoorva Khare (Indian Institute of Science\, India) DTSTART:20201118T120000Z DTEND:20201118T130000Z DTSTAMP:20260423T052957Z UID:FAOT/1 DESCRIPTION:Title: Ent rywise positivity preservers in fixed dimension: I\nby Apoorva Khare ( Indian Institute of Science\, India) as part of Functional Analysis and Op erator Theory Webinar\n\n\nAbstract\nWhich functions preserve positive sem idefiniteness (psd) when applied entrywise to\nthe entries of psd matrices ? This question has a long history beginning with Schur\,\nSchoenberg\, an d Rudin\, who classified the positivity preservers of matrices of all dime nsions. The study of positivity preservers in fixed dimension is harder\, and a complete\ncharacterization remains elusive to date. In fact until re cent work\, it was not known if\nthere exists any analytic preserver with negative coefficients.\n\nIn my first talk\, I will explain the classical history and modern motivations of this\nproblem\, followed by a “restric ted” solution in every dimension. Central to the proof\nare novel determ inantal identities involving Schur polynomials. I will conclude with a\nfe w outstanding questions.\n\n(Based on two papers: with Alexander Belton\, Dominique Guillot\, and Mihai Putinar\, Adv. Math. 2016\; and with Terence Tao\, Amer. J. Math.\, in press.)\n LOCATION:https://researchseminars.org/talk/FAOT/1/ END:VEVENT END:VCALENDAR