BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thiago Carvalho Corso (Stuttgart) DTSTART:20241126T131500Z DTEND:20241126T140000Z DTSTAMP:20260423T021258Z UID:MAS-MP/83 DESCRIPTION:Title: Improvements on the Lieb-Thirring and Cwikel-Lieb-Rozenblum bounds via a t hree lines lemma\nby Thiago Carvalho Corso (Stuttgart) as part of Muni ch-Copenhagen-Santiago Mathematical Physics seminar\n\n\nAbstract\nIn this talk I will present some recent improvements [1\,2] on the best-known upp er bounds for the optimal constants in the Lieb-Thirring (LT) and Cwikel-L ieb-Rozenblum (CLR) inequalities. These improvements were obtained by expl icitly solving an interesting family of variational problems\, whose conne ction with the LT and CLR inequalities has recently been established in [3 ] and [4]\, respectively. To obtain the explicit solutions\, we first refo rmulate these variational problems as an interpolation-like inequality alo ng three parallel lines in the complex plane\, for certain spaces of holom orphic functions. We then explicitly compute the optimizers for these inte rpolation inequalities by combining some techniques of complex\, Fourier\, and convex analysis.\n\n\nReferences:\n[1] Corso and Ried - On a variatio nal problem related to the Cwikel-LiebRozenblum and Lieb-Thirring inequali ties\n- https://arxiv.org/abs/2403.04347\n[2] Corso - A generalized three lines lemma in Hardy-like spaces\n- https://arxiv.org/abs/2407.10117\n[3] Frank\, Hundertmark\, Jex\, and Nam - The Lieb-Thirring inequality revisit ed\n- https://ems.press/journals/jems/articles/666342\n[4] Hundertmark\, K unstmann\, Ried\, and Vugalter - Cwikel’s bound reloaded\n- https://link .springer.com/article/10.1007/s00222-022-01144-7\n LOCATION:https://researchseminars.org/talk/MAS-MP/83/ END:VEVENT END:VCALENDAR