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SUMMARY:Euan Spence (Bath)
DTSTART;VALUE=DATE-TIME:20200528T140000Z
DTEND;VALUE=DATE-TIME:20200528T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T213249Z
UID:LANS/1
DESCRIPTION:Title: Res
olution of a long-standing open question in the theory of boundary integra
l equations for Laplace's equation\nby Euan Spence (Bath) as part of L
ondon analysis seminar\n\n\nAbstract\nThis talk is concerned with the theo
ry of boundary integral equations for Laplace's equation on Lipschitz doma
ins. The theory for these equations in the space L^2(\\Gamma)\, where \\Ga
mma is the boundary of the domain\, was developed in the 1980s by Calderon
\, Coifman\, McIntosh\, Meyer\, and Verchota. However\, the following ques
tion has remained open: can the standard second-kind integral equations\,
posed in L^2(\\Gamma)\, be written as the sum of a coercive operator and a
compact operator when \\Gamma is only assumed to be Lipschitz\, or even L
ipschitz polyhedral? The practical importance of this question is that the
convergence analysis the Galerkin method applied to these integral equati
ons relies on this "coercive + compact" property holding. This talk will d
escribe joint work with Simon Chandler-Wilde (University of Reading) that
answers this question.\n
LOCATION:https://researchseminars.org/talk/LANS/1/
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SUMMARY:Lyonell Boulton (Heriot Watt)
DTSTART;VALUE=DATE-TIME:20200604T140000Z
DTEND;VALUE=DATE-TIME:20200604T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T213249Z
UID:LANS/2
DESCRIPTION:Title: Lin
ear Completeness for Non-linear Spectral Problems\nby Lyonell Boulton
(Heriot Watt) as part of London analysis seminar\n\n\nAbstract\nThis talk
concerns the question of completeness for families of eigenfunctions assoc
iated to non-linear eigenvalue problems. After presenting the general sett
ing\, I will comment on several directions of progress about this question
for a few model equations on a segment. These include versions of the non
-linear Laplacian eigenvalue problem\, the non-linear Schrödinger and p
erhaps a couple of other artificial\, but interesting\, cases. During the
talk it will become evident that the question of completeness is intimatel
y related with deep results about the basis properties of dilated periodic
functions. Some of these date back to the pioneering work of Beurling in
the mid 1950s and a remarkable framework developed by Hedenmalm\, Lindqvis
t and Seip in the 1990s.\n
LOCATION:https://researchseminars.org/talk/LANS/2/
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BEGIN:VEVENT
SUMMARY:Jeffrey Galkowski (UCL)
DTSTART;VALUE=DATE-TIME:20200430T140000Z
DTEND;VALUE=DATE-TIME:20200430T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T213249Z
UID:LANS/3
DESCRIPTION:Title: Int
erior behavior of Steklov eigenfunctions\nby Jeffrey Galkowski (UCL) a
s part of London analysis seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LANS/3/
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SUMMARY:Ben Krause (Princeton)
DTSTART;VALUE=DATE-TIME:20200507T140000Z
DTEND;VALUE=DATE-TIME:20200507T150000Z
DTSTAMP;VALUE=DATE-TIME:20240328T213249Z
UID:LANS/4
DESCRIPTION:Title: Poi
ntwise Convergence of Multiple Ergodic Averages\nby Ben Krause (Prince
ton) as part of London analysis seminar\n\n\nAbstract\nBeginning with the
basics of pointwise ergodic theory\, I will discuss my forthcoming proof o
f the Furstenberg conjecture\, on the pointwise convergence of the bilinea
r ergodic averages\, $\\frac{1}{N} \\sum_{n \\leq N} T^n f T^{n^2} g\,$ wh
ere $f\,g \\in L^{\\infty}(X)$ are bounded functions on a probability spac
e $(X\,\\mu)$\, and $T:X \\to X$ is a measure-preserving transformation. J
oint work with Mariusz Mirek (Rutgers) and Terence Tao (UCLA).\n
LOCATION:https://researchseminars.org/talk/LANS/4/
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