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:Towards a multivariable Wiener-Hopf method: Lectur
e 1 - Raphael Assier (University of Manchester)\;
Andrey Shanin (Moscow State University)
DTSTART;TZID=Europe/London:20190806T120000
DTEND;TZID=Europe/London:20190806T131500
UID:TALK128101AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128101
DESCRIPTION:A multivariable\, in particular two complex
variables (2D)\, Wiener-Hopf (WH) method is one of
the desired generalisations of the classical and
celebrated WH technique that are easily conceived
but very hard to implement (the second one\, indee
d\, is the matrix WH). A 2D WH method\, could pote
ntially be used e.g. for finding a solution to the
canonical problem of diffraction by a quarter-pla
ne.  \;
Unfortunately\
, multidimensional complex analysis seems to be wa
y more complicated than complex analysis of a sing
le variable. There exists a number of powerful the
orems in it\, but they are organised into several
disjoint theories\, and\, generally all of them ar
e far from the needs of WH. In this mini-lecture
course\, we hope to introduce topics in complex an
alysis of several variables that we think are impo
rtant for a generalisation of the WH technique. We
will focus on the similarities and differences be
tween functions of one complex variable and functi
ons of two complex variables. Elements of differen
tial forms and homotopy theory will be addressed.
We will start by reviewing some k
nown attempts at building a 2D WH and explain why
they were not successful. The framework of Fourier
transforms and analytic functions in 2D will be i
ntroduced\, leading us naturally to discuss multid
imensional integration contours and their possible
deformations. One of our main focus will be on po
lar and branch singularity sets and how to describ
e how a multidimensional contour bypasses these si
ngularities. We will explain how multidimensional
integral representation can be used in order to pe
rform an analytical continuation of the unknowns o
f a 2D functional equation and why we believe it t
o be important. Finally\, time permitting\, we wil
l discuss the branching structure of complex integ
rals depending on some parameters and introduce th
e so-called Picard-Lefschetz formulae.&rdquo\;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR