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CATEGORIES:Lecture
DESCRIPTION:'On the Pierce-Birkhoff Conjecture' - \n\nWhat real-valued func
tions can be expressed using addition\, scalar multiplication and absolute
value? The answer is that any piecewise linear function (with finitely many
pieces) \(f:\mathbb{R}^n\to \mathbb{R}\) can be expressed with these notat
ional resources. How about the same question if we extend our notational re
sources by including multiplication? Evidently\, any function that can be
so expressed is piecewise polynomial. Is it the case\, conversely\, that ev
ery piecewise polynomial function on \(\mathbb{R}^n\) can be so expressed?
The answer is Yes for \(n=1\) and \(n=2\)\, but remarkably we do not know t
he answer for \(n\geq 3\). In 1956\, Garret Birkhoff and Richard Pierce co
njectured Yes\, for all n. This problem has had a significant impact on my
career as a mathematician. In this talk\, I'll sketch out important mathema
tics related to this problem and tell you about some of the people I've met
and some of the experiences I've had while working on it.\n\nJames Madden
graduated from Reed College in 1974 with a degree in Anthropol-ogy. He obta
ined his Ph.D. in Mathematics from Wesleyan University in 1983. He is prese
ntly the Patricia Hewlett Bodin Distinguished Professor of Mathematics at L
ouisiana State University.
DTEND:20191115T013000Z
DTSTAMP:20200123T053209Z
DTSTART:20191115T004000Z
GEO:45.480972;-122.630792
LOCATION:Eliot Hall\, 314
SEQUENCE:0
SUMMARY:Math Colloquium: James Madden '74\, Louisiana State University
UID:tag:localist.com\,2008:EventInstance_31343739752775
URL:https://events.reed.edu/event/math_colloquium_james_madden_74_louisiana
_state_university
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