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CATEGORIES:Analysis seminar
SUMMARY:Transversality in Harmonic Analysis and the Brasca
mp–Lieb Inequalities - Jennifer Duncan (Mathematic
s) University of Birmingham
DTSTART:20221017T140000Z
DTEND:20221017T150000Z
UID:TALK5023AT
URL:/talk/index/5023
DESCRIPTION:In modern harmonic analysis\, there is a ubiquity
of operators whose functional-analytic properties
depend on the geometric properties of an underlyin
g submanifold\, such as Fourier extension operator
s and Radon-like transforms. In the analysis of th
e boundedness of such operators\, it is often usef
ul to employ a linear-to-multilinear reduction so
that one may appeal to a multilinearised version o
f the linear estimate one would like to obtain. Th
ese multilinear estimates usually require that the
submanifolds involved are uniformly transversal i
n some suitable sense\, however\, standard linear
algebra tools are sometimes insufficient to captur
e an appropriately general notion of transversalit
y for the estimates in which we are interested. Br
ascamp–Lieb inequalities offer a robust framework
for understanding this higher-order notion transve
rsality in a manner that is well-suited to applica
tions in harmonic analysis and pdes. In my talk\,
I shall introduce the notion of a Brascamp–Lieb in
equality\, describe the broader role they play in
the subject\, and go on to discuss the topic of no
nlinear Brascamp–Lieb inequalities\, a recent vari
ant that generalises this framework to the manifol
d setting.\n
LOCATION:WATN-LT C (G24)
CONTACT:Yuzhao Wang
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