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:20260404T100033Z 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 Rese arch Webinar\n\n\nAbstract\nWe shall try to draw a quite unexpected connec tion between Kalton and Roberts' work in the theory of twisted sums of Ban ach spaces (and quasi-linear maps) that originated with the construction o f twisted Hilbert spaces and fine-tuning certain optimisation algorithms. Kalton and Roberts [Trans. Amer. Math. Soc. 1983] proved a stability resul t for 1-additive maps asserting that there exists a universal constant K n ot smaller than 44.5 such that for any set algebra F\, for every scalar-va lued 1-additive map f defined thereon\, there is a 0-additive map (a finit ely additive signed measure) whose distance to f is at most K. Pawlik [Col loq. Math. 1987] noticed that in general K cannot be smaller than 1.5. We shall present a class of positive 1-additive maps\, which witnesses that K cannot be smaller than 3. If time permits\, we shall mention certain resu lts due to Feige\, Feldman\, and Talgam-Cohen [SIAM J. Comput. 2020] illus trating the sensitivity of certain machine-learning algorithms to estimate s for K. \n\nThis is joint work with M. Gnacik (UoP) and M. Guzik (UBS) [P roc. Amer. Math. Soc. 2020+].\n LOCATION:https://stable.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:20260404T100033Z UID:PortMATHS/2 DESCRIPTION:Title: On delocalization in the six-vertex model\nby Marcin Lis (Fac ulty of Mathematics\, University of Vienna\, Austria) as part of Portsea M aths Research Webinar\n\n\nAbstract\nWe show that the six-vertex model wit h parameter $c \\in [\\sqrt{3}\,2]$ on a square lattice torus has an ergod ic infinite-volume limit as the size of the torus grows to infinity. Moreo ver we prove that for $ c \\in \\left[\\sqrt{2 + \\sqrt{2}}\, 2 \\right]$\ , the associated height function on $\\mathbb{Z}^2$ has unbounded variance .\nThe proof relies on an extension of the Baxter–Kelland–Wu represent ation of the six-vertex model to multi-point correlation functions of the associated spin model. Other crucial ingredients are the uniqueness and pe rcolation 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://stable.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:20260404T100033Z UID:PortMATHS/3 DESCRIPTION:Title: My life in quantum probability\nby Robin Hudson (Department o f Mathematical Sciences\, Loughborough University\, UK) as part of Portsea Maths Research Webinar\n\n\nAbstract\nAfter an introduction explaining ho w quantum probability differs from classical probability\, which includes a conservative quantum notion of independence which differentiates quantu m from free probability\, I will describe some of my own contributions to the subject\, including non-negativity of Wigner quasi-probability densiti es\, a quantum central limit theorem and quantum planar Brownian motions\n LOCATION:https://stable.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:20260404T100033Z UID:PortMATHS/4 DESCRIPTION:Title: Moment identities for Poisson stochastic integrals and applicatio ns\nby Nicolas Privault (Division of Mathematical Sciences School of P hysical and Mathematical Sciences Nanyang Technological University\, Singa pore) as part of Portsea Maths Research Webinar\n\n\nAbstract\nIn this tal k\, we will discuss nonlinear extensions of the Slivnyak-Mecke formula for the computation of the expected value of functionals of Poisson point pro cesses. Applications will be given to graph connectivity in the random-con nection model\, and to distribution estimation for random sets in stochast ic geometry.\n LOCATION:https://stable.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:20260404T100033Z UID:PortMATHS/7 DESCRIPTION:Title: Preservers for positive-semidefinite and totally positive matrice s\nby Alexander Belton (Department of Mathematics and Statistics\, Lan caster University\, UK) as part of Portsea Maths Research Webinar\n\n\nAbs tract\nThe Schur product theorem implies that the set of positive-semidefi nite matrices is invariant under the entrywise application of any absolute ly monotonic function. Shoenberg's work shows that the converse is also tr ue: a function which preserves positive semidefiniteness for matrices of a rbitrary size is necessarily absolutely monotonic. For totally positive ma trices\, the class of preservers is much smaller\, being only the linear h omotheties.\n\nThe situation is more complex for matrices of a fixed size\ , or when the class of matrices under study has some additional structure. This talk will address these questions\, including the cases of Hankel an d Toeplitz matrices.\n\nThis is joint work with Dominique Guillot (Univers ity of Delaware)\, Apoorva Khare (Indian Institute of Science\, Bangalore) and Mihai Putinar (University of California at Santa Barbara and Newcastl e University).\n LOCATION:https://stable.researchseminars.org/talk/PortMATHS/7/ END:VEVENT END:VCALENDAR