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PRODID:Mathematics Seminar Calendar
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UID:20180318T132739-7231@math.msu.edu
DTSTAMP:20180318T132739Z
SUMMARY:Probabilistic scattering for the 4D energy-critical defocusing nonlinear wave equation
DESCRIPTION:Speaker\: Jonas Lührmann\r\nWe consider the Cauchy problem for the energy-critical defocusing \r\nnonlinear wave equation in four space dimensions. It is known that for \r\ninitial data at energy regularity, the solutions exist globally in time \r\nand scatter to free waves. However, the problem is ill-posed for initial \r\ndata at super-critical regularity, i.e. for regularities below the \r\nenergy regularity.\r\nIn this talk we study the super-critical data regime for this Cauchy \r\nproblem from a probabilistic point of view, using a randomization \r\nprocedure that is based on a unit-scale decomposition of frequency \r\nspace. We will present an almost sure global existence and scattering \r\nresult for randomized radially symmetric initial data of super-critical \r\nregularity. This is the first almost sure scattering result for an \r\nenergy-critical dispersive or hyperbolic equation for scaling \r\nsuper-critical initial data.\r\nThe main novelties of our proof are the introduction of an approximate \r\nMorawetz estimate to the random data setting and new large deviation \r\nestimates for the free wave evolution of randomized radially symmetric data.\r\n\r\nThis is joint work with Ben Dodson and Dana Mendelson.
LOCATION:C304 Wells Hall
DTSTART:20180125T160000Z
DTEND:20180125T170000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=7231
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UID:20180318T132739-10276@math.msu.edu
DTSTAMP:20180318T132739Z
SUMMARY:Quantization of conductance in gapped interacting systems
DESCRIPTION:Speaker\: Martin Fraas, Virginia Tech\r\nI will present two closely connected results. The first is the linear response theory in gapped interacting systems, and a proof of the associated Kubo formula. The second is a short proof of the quantization of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus.
LOCATION:C304 Wells Hall
DTSTART:20180215T160000Z
DTEND:20180215T170000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=10276
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UID:20180318T132739-13294@math.msu.edu
DTSTAMP:20180318T132739Z
SUMMARY:Dependence of the density of states on the probability distribution for discrete random Schrödinger operators
DESCRIPTION:Speaker\: Chris Marx, Oberlin College\r\nWe prove the Hölder-continuity of the density of states measure (DOSm) and the integrated density of states (IDS) with respect to the probability distribution for discrete random Schrödinger operators with a finite-range potential. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli distribution converge to the corresponding quantities for the Bernoulli-Anderson model. Other applications of the techniques are given to the dependency of the DOSm and IDS on the disorder, and the continuity of the Lyapunov exponent in the weak-disorder regime. The talk is based on recent joint work with Peter Hislop (Univ. of Kentucky).\r\n\r\n
LOCATION:C304 Wells Hall
DTSTART:20180315T150000Z
DTEND:20180315T160000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13294
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