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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:20240910T013856Z
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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BEGIN:VEVENT
SUMMARY:Marcin Lis (Faculty of Mathematics\, University of Vienna\, Austri
a)
DTSTART;VALUE=DATE-TIME:20200603T130000Z
DTEND;VALUE=DATE-TIME:20200603T140000Z
DTSTAMP;VALUE=DATE-TIME:20240910T013856Z
UID:PortMATHS/2
DESCRIPTION:Title: On delocalization in the six-vertex model\nby Marcin Lis (Faculty of
Mathematics\, University of Vienna\, Austria) as part of Portsea Maths Re
search Webinar\n\n\nAbstract\nWe show that the six-vertex model with param
eter $c \\in [\\sqrt{3}\,2]$ on a square lattice torus has an ergodic infi
nite-volume limit as the size of the torus grows to infinity. Moreover we
prove that for $ c \\in \\left[\\sqrt{2 + \\sqrt{2}}\, 2 \\right]$\, the a
ssociated height function on $\\mathbb{Z}^2$ has unbounded variance.\nThe
proof relies on an extension of the Baxter–Kelland–Wu representation o
f the six-vertex model to multi-point correlation functions of the associa
ted spin model. Other crucial ingredients are the uniqueness and percolati
on properties of the critical random cluster measure for $q \\in [1\, 4]$\
, and recent results relating the decay of correlations in the spin model
with the delocalization of the height function.\n
LOCATION:https://researchseminars.org/talk/PortMATHS/2/
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BEGIN:VEVENT
SUMMARY:Robin Hudson (Department of Mathematical Sciences\, Loughborough U
niversity\, UK)
DTSTART;VALUE=DATE-TIME:20200617T130000Z
DTEND;VALUE=DATE-TIME:20200617T140000Z
DTSTAMP;VALUE=DATE-TIME:20240910T013856Z
UID:PortMATHS/3
DESCRIPTION:Title: My life in quantum probability\nby Robin Hudson (Department of Mathe
matical Sciences\, Loughborough University\, UK) as part of Portsea Maths
Research Webinar\n\n\nAbstract\nAfter an introduction explaining how quan
tum probability differs from classical probability\, which includes a cons
ervative quantum notion of independence which differentiates quantum from
free probability\, I will describe some of my own contributions to the sub
ject\, including non-negativity of Wigner quasi-probability densities\, a
quantum central limit theorem and quantum planar Brownian motions\n
LOCATION:https://researchseminars.org/talk/PortMATHS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Privault (Division of Mathematical Sciences School of Phys
ical and Mathematical Sciences Nanyang Technological University\, Singapor
e)
DTSTART;VALUE=DATE-TIME:20200624T130000Z
DTEND;VALUE=DATE-TIME:20200624T140000Z
DTSTAMP;VALUE=DATE-TIME:20240910T013856Z
UID:PortMATHS/4
DESCRIPTION:Title: Moment identities for Poisson stochastic integrals and applications\
nby Nicolas Privault (Division of Mathematical Sciences School of Physical
and Mathematical Sciences Nanyang Technological University\, Singapore) a
s part of Portsea Maths Research Webinar\n\n\nAbstract\nIn this talk\, we
will discuss nonlinear extensions of the Slivnyak-Mecke formula for the co
mputation of the expected value of functionals of Poisson point processes.
Applications will be given to graph connectivity in the random-connection
model\, and to distribution estimation for random sets in stochastic geom
etry.\n
LOCATION:https://researchseminars.org/talk/PortMATHS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Belton (Department of Mathematics and Statistics\, Lanca
ster University\, UK)
DTSTART;VALUE=DATE-TIME:20200722T130000Z
DTEND;VALUE=DATE-TIME:20200722T140000Z
DTSTAMP;VALUE=DATE-TIME:20240910T013856Z
UID:PortMATHS/7
DESCRIPTION:Title: Preservers for positive-semidefinite and totally positive matrices\n
by Alexander Belton (Department of Mathematics and Statistics\, Lancaster
University\, UK) as part of Portsea Maths Research Webinar\n\n\nAbstract\n
The Schur product theorem implies that the set of positive-semidefinite ma
trices is invariant under the entrywise application of any absolutely mono
tonic function. Shoenberg's work shows that the converse is also true: a f
unction which preserves positive semidefiniteness for matrices of arbitrar
y size is necessarily absolutely monotonic. For totally positive matrices\
, the class of preservers is much smaller\, being only the linear homothet
ies.\n\nThe situation is more complex for matrices of a fixed size\, or wh
en the class of matrices under study has some additional structure. This t
alk will address these questions\, including the cases of Hankel and Toepl
itz matrices.\n\nThis is joint work with Dominique Guillot (University of
Delaware)\, Apoorva Khare (Indian Institute of Science\, Bangalore) and Mi
hai Putinar (University of California at Santa Barbara and Newcastle Unive
rsity).\n
LOCATION:https://researchseminars.org/talk/PortMATHS/7/
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