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:20260422T212604Z 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 BEGIN:VEVENT SUMMARY:Marcin Lis (Faculty of Mathematics\, University of Vienna\, Austri a) DTSTART:20200603T130000Z DTEND:20200603T140000Z DTSTAMP:20260422T212604Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Robin Hudson (Department of Mathematical Sciences\, Loughborough U niversity\, UK) DTSTART:20200617T130000Z DTEND:20200617T140000Z DTSTAMP:20260422T212604Z 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:20200624T130000Z DTEND:20200624T140000Z DTSTAMP:20260422T212604Z 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:20200722T130000Z DTEND:20200722T140000Z DTSTAMP:20260422T212604Z 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/ END:VEVENT END:VCALENDAR