BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tomasz Kania (Institute of Mathematics\, Czech Academy of Sciences \, Czech Republic) DTSTART:20200527T130000Z DTEND:20200527T140000Z DTSTAMP:20260423T024453Z UID:PortMATHS/1 DESCRIPTION:Title: Estimating Kalton's constant: from twisted sums of Banach spaces to fine -tuning algorithms\nby Tomasz Kania (Institute of Mathematics\, Czech Academy of Sciences\, Czech Republic) as part of Portsea Maths Research We binar\n\n\nAbstract\nWe shall try to draw a quite unexpected connection be tween Kalton and Roberts' work in the theory of twisted sums of Banach spa ces (and quasi-linear maps) that originated with the construction of twist ed Hilbert spaces and fine-tuning certain optimisation algorithms. Kalton and Roberts [Trans. Amer. Math. Soc. 1983] proved a stability result for 1 -additive maps asserting that there exists a universal constant K not smal ler than 44.5 such that for any set algebra F\, for every scalar-valued 1- additive map f defined thereon\, there is a 0-additive map (a finitely add itive signed measure) whose distance to f is at most K. Pawlik [Colloq. Ma th. 1987] noticed that in general K cannot be smaller than 1.5. We shall p resent a class of positive 1-additive maps\, which witnesses that K cannot be smaller than 3. If time permits\, we shall mention certain results due to Feige\, Feldman\, and Talgam-Cohen [SIAM J. Comput. 2020] illustrating the sensitivity of certain machine-learning algorithms to estimates for K . \n\nThis is joint work with M. Gnacik (UoP) and M. Guzik (UBS) [Proc. Am er. Math. Soc. 2020+].\n LOCATION:https://researchseminars.org/talk/PortMATHS/1/ END:VEVENT END:VCALENDAR