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SUMMARY:Euan Spence (Bath)
DTSTART:20200528T140000Z
DTEND:20200528T150000Z
DTSTAMP:20260404T111007Z
UID:LANS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/LANS/
 1/">Resolution of a long-standing open question in the theory of boundary 
 integral equations for Laplace's equation</a>\nby Euan Spence (Bath) as pa
 rt of London analysis seminar\n\n\nAbstract\nThis talk is concerned with t
 he theory of boundary integral equations for Laplace's equation on Lipschi
 tz domains. The theory for these equations in the space L^2(\\Gamma)\, whe
 re \\Gamma is the boundary of the domain\, was developed in the 1980s by C
 alderon\, Coifman\, McIntosh\, Meyer\, and Verchota. However\, the followi
 ng question has remained open: can the standard second-kind integral equat
 ions\, posed in L^2(\\Gamma)\, be written as the sum of a coercive operato
 r and a compact operator when \\Gamma is only assumed to be Lipschitz\, or
  even Lipschitz polyhedral? The practical importance of this question is t
 hat the convergence analysis the Galerkin method applied to these integral
  equations relies on this "coercive + compact" property holding. This talk
  will describe joint work with Simon Chandler-Wilde (University of Reading
 ) that answers this question.\n
LOCATION:https://stable.researchseminars.org/talk/LANS/1/
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BEGIN:VEVENT
SUMMARY:Lyonell Boulton (Heriot Watt)
DTSTART:20200604T140000Z
DTEND:20200604T150000Z
DTSTAMP:20260404T111007Z
UID:LANS/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/LANS/
 2/">Linear Completeness for Non-linear Spectral Problems</a>\nby Lyonell B
 oulton (Heriot Watt) as part of London analysis seminar\n\n\nAbstract\nThi
 s talk concerns the question of completeness for families of eigenfunction
 s associated to non-linear eigenvalue problems. After presenting the gener
 al setting\, I will comment on several directions of progress about this q
 uestion for a few model equations on a segment. These include versions of 
 the non-linear Laplacian eigenvalue problem\, the non-linear Schrödinge
 r and perhaps a couple of other artificial\, but interesting\, cases. Duri
 ng the talk it will become evident that the question of completeness is in
 timately related with deep results about the basis properties of dilated p
 eriodic functions. Some of these date back to the pioneering work of Beurl
 ing in the mid 1950s and a remarkable framework developed by Hedenmalm\, L
 indqvist and Seip in the 1990s.\n
LOCATION:https://stable.researchseminars.org/talk/LANS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Galkowski (UCL)
DTSTART:20200430T140000Z
DTEND:20200430T150000Z
DTSTAMP:20260404T111007Z
UID:LANS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/LANS/
 3/">Interior behavior of Steklov eigenfunctions</a>\nby Jeffrey Galkowski 
 (UCL) as part of London analysis seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LANS/3/
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BEGIN:VEVENT
SUMMARY:Ben Krause (Princeton)
DTSTART:20200507T140000Z
DTEND:20200507T150000Z
DTSTAMP:20260404T111007Z
UID:LANS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/LANS/
 4/">Pointwise Convergence of Multiple Ergodic Averages</a>\nby Ben Krause 
 (Princeton) as part of London analysis seminar\n\n\nAbstract\nBeginning wi
 th the basics of pointwise ergodic theory\, I will discuss my forthcoming 
 proof of the Furstenberg conjecture\, on the pointwise convergence of the 
 bilinear ergodic averages\, $\\frac{1}{N} \\sum_{n \\leq N} T^n f T^{n^2} 
 g\,$ where $f\,g \\in L^{\\infty}(X)$ are bounded functions on a probabili
 ty space $(X\,\\mu)$\, and $T:X \\to X$ is a measure-preserving transforma
 tion. Joint work with Mariusz Mirek (Rutgers) and Terence Tao (UCLA).\n
LOCATION:https://stable.researchseminars.org/talk/LANS/4/
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