BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Orthogonal polynomials\, singular integrals\, and
solving Riemann&\;ndash\;Hilbert problems: Lect
ure 2 - Sheehan Olver (Imperial College London)
DTSTART;TZID=Europe/London:20190809T120000
DTEND;TZID=Europe/London:20190809T131500
UID:TALK128311AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128311
DESCRIPTION:Orthogonal polynomials are fundamental tools
in numerical methods\, including for singular int
egral equations. A known result is that Cauchy tra
nsforms of weighted orthogonal polynomials satisfy
the same three-term recurrences as the orthogonal
polynomials themselves for n >\; 0. This basic
fact leads to extremely effective schemes of calcu
lating singular integrals and discretisations of s
ingular integral equations that converge spectrall
y fast (faster than any algebraic power). Applicat
ions considered include matrix Riemann&ndash\;Hilb
ert problems on contours consisting of interconnec
ted line segments and Wiener&ndash\;Hopf problems.
This technique is extendible to calculating singu
lar integrals with logarithmic kernels\, with appl
ications to Green&rsquo\;s function reduction of P
DEs such as the Helmholtz equation. \;

Using novel change-of-variable formulae
\, we will adapt these results to tackle singular
integral equations on more general smooth arcs\, g
eometries with corners\, and Wiener&ndash\;Hopf pr
oblems whose solutions only decay algebraically.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
END:VEVENT
END:VCALENDAR