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SUMMARY:Tomasz Kania (Institute of Mathematics\, Czech Academy of Sciences
\, Czech Republic)
DTSTART;VALUE=DATE-TIME:20200527T130000Z
DTEND;VALUE=DATE-TIME:20200527T140000Z
DTSTAMP;VALUE=DATE-TIME:20240522T210821Z
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/
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