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DTSTART;TZID=America/Halifax:20201106T160000
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DTSTAMP:20201108T225930Z
CREATED:20200904T115630Z
LAST-MODIFIED:20201108T225930Z
UID:5470-1604678400-1604682000@aarms.math.ca
SUMMARY:Dalhousie-AARMS AAMP Seminar: Reem Yassawi (Open University\, London)
DESCRIPTION:Title: Some tame or wild Cantor dynamical systems\n Abstract: A topological dynamical system is a pair  where  is a compact metric spaces and  is a group or semigroup acting continuously on . One algebraic invariant of a such a dynamical system is the Ellis semigroup.  The Ellis semigroup  of a topological dynamical system is defined to be the compactification of the action  in the topology of pointwise convergence on the space of all function .  Tameness is a concept whose roots date back to Rosenthal’s  embedding theorem\, which says that if a sequence in  does not have a weakly Cauchy subsequence\, then it must be a sequence on unit vectors in .  Köhler linked the concept of tameness to the Ellis semigroup.  A system is tame if its Ellis semigroup has size at most the continuum.  Non-tame systems are very far from tame\, as they must contain a copy of \, the Stone-Cech compactification of . \nIn this talk\, I will briefly survey the properties of the Ellis semigroup that make it an interesting object to study\, and discuss recent developments concerning tameness.  I will then discuss Toeplitz shifts\, which themselves have been studied extensively in this context and is the subject of some joint work with G. Fuhrmann and J. Kellendonk. \nThe Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend\, please email the organizers for connection details.
URL:https://aarms.math.ca/event/dalhousie-aarms-aamp-seminar-2020-10-16-2-2-2-2/
LOCATION:Zoom seminar
CATEGORIES:AAMP Seminar
ORGANIZER;CN="Suresh Eswarathasan":MAILTO:sr766936@dal.ca
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DTSTART;TZID=America/Halifax:20201127T160000
DTEND;TZID=America/Halifax:20201127T170000
DTSTAMP:20201123T152316Z
CREATED:20200904T115630Z
LAST-MODIFIED:20201123T152316Z
UID:5472-1606492800-1606496400@aarms.math.ca
SUMMARY:Dalhousie-AARMS AAMP Seminar: Graham Cox (Memorial University)
DESCRIPTION:Title: Nodal deficiency via equipartition energy functionals and the Dirichlet-to-Neumann map\nAbstract: A classic result in differential equations is that the nth eigenfunction\nof a Sturm-Liouville boundary value problem has precisely n-1 zeros.\nCourant’s nodal domain theorem provides a natural generalization of this\nresult to higher dimensions\, but it is generally not sharp. The lack of\nsharpness is measured by the “nodal deficiency” of an eigenfunction.\nDespite over a century of intensive study\, this quantity is still not\nvery well understood. \nThe first explicit formula for the nodal deficiency was obtained in 2012\nby Berkolaiko\, Kuchment and Smilansky\, using an energy functional\ndefined on the space of equipartitions. More recently\, with Jones and\nMarzuola\, I obtained another formula for the nodal deficiency\, in terms\nof Dirichlet-to-Neumann operators defined on the eigenfunction’s nodal\ndomains. While originally derived using symplectic methods\, this result\ncan also be understood using the spectral flow generated by a family of\nboundary conditions imposed on the nodal set. In this talk I will\ndescribe this flow\, and explain how it provides a concrete mechanism by\nwhich low energy eigenfunctions do or do not contribute to the nodal\ndeficiency. I will also describe recent progress relating these two\nformulas for the nodal deficiency\, and hint at some applications to the\ntheory of spectral minimal partitions. \nThis talk represents joint work with Thomas Beck\, Gregory Berkolaiko\,\nIsabel Bors\, Yaiza Canzani\, Grace Conte\, Christopher Jones and Jeremy\nMarzuola. \nThe Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend\, please email the organizers for connection details.
URL:https://aarms.math.ca/event/dalhousie-aarms-aamp-seminar-2020-10-16-2-2-2/
LOCATION:Zoom seminar
CATEGORIES:AAMP Seminar
ORGANIZER;CN="Suresh Eswarathasan":MAILTO:sr766936@dal.ca
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