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TZID:America/Chicago
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DTSTART:20181104T020000
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DTSTART:20190310T020000
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UID:calendar.23052.field_event_date_2.0@math.wustl.edu
CREATED:20181114T223103Z
DESCRIPTION:Abstract: The averages of a locally integrable function over fa
milies of shrinking Euclidean balls converge almost everywhere: this is th
e Lebesgue differentiation theorem. A fundamental conjecture\, attributed
to Antoni Zygmund\, is whether a square integrable function on the plane m
ay be differentiated by Lipschitz families of lines: this is equivalent to
L^2 bounds for the maximal averaging operator along a Lipschitz vector fi
eld. The operator obtained by replacing the maximal average by a direction
al singular integral is the object of a companion conjecture due to Elias
Stein. Directional singular integrals share deep ties to other central obj
ects in Analysis: most notably\, the pointwise convergence of Fourier seri
es and the polygonal summation problem. I will discuss recent progress on
Stein’s conjecture and on finitary models of both problems. In particular\
, I will focus on the L^2 sharp bound for directional maximal averages alo
ng finite subsets of algebraic varieties of arbitrary codimension\, and on
its proof involving polynomial partitioning techniques. This result is in
collaboration with Ioannis Parissis (University of Basque Country).\n\n
\n\nHost: Brett Wick\n\nTea will be served @ 3:45 in room 200
DTSTART;TZID=America/Chicago:20181206T161500
DTEND;TZID=America/Chicago:20181206T171500
LAST-MODIFIED:20181114T223103Z
SUMMARY:'Maximal averages and singular integrals along vector fields'
URL;TYPE=URI:https://math.wustl.edu/events/maximal-averages-and-singular-in
tegrals-along-vector-fields
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