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SUMMARY:Euan Spence (Bath)
DTSTART:20200528T140000Z
DTEND:20200528T150000Z
DTSTAMP:20260422T225756Z
UID:LANS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LANS/1/">Res
 olution of a long-standing open question in the theory of boundary integra
 l equations for Laplace's equation</a>\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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BEGIN:VEVENT
SUMMARY:Lyonell Boulton (Heriot Watt)
DTSTART:20200604T140000Z
DTEND:20200604T150000Z
DTSTAMP:20260422T225756Z
UID:LANS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LANS/2/">Lin
 ear Completeness for Non-linear Spectral Problems</a>\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:20200430T140000Z
DTEND:20200430T150000Z
DTSTAMP:20260422T225756Z
UID:LANS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LANS/3/">Int
 erior behavior of Steklov eigenfunctions</a>\nby Jeffrey Galkowski (UCL) a
 s part of London analysis seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/LANS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Krause (Princeton)
DTSTART:20200507T140000Z
DTEND:20200507T150000Z
DTSTAMP:20260422T225756Z
UID:LANS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LANS/4/">Poi
 ntwise Convergence of Multiple Ergodic Averages</a>\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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