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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:(Reception\, Irrani Hall Foyer: 3:30pm-4:00pm)\n\nRichard Stanl
ey\nEmeritus Professor of Mathematics\, MIT\n\nShort abstract:\nAn increasi
ng subsequence of a permutation a_1\, a_2\, ... \, a_n of 1\,2\, ... \, n i
s a subsequence b_1\,b_2\, ... \, b_k satisfying b_1 < b_2 < ... < b_k\,
and similarly for decreasing subsequence. The earliest result in this area
is due to Erdös and Szekeres in 1935: any permutation of 1\,2\, ... \, pq +
1 has an increasing subsequence of length p+1 or a decreasing subsequence
of length q+1. This result turns out to be closely connected to the RSK al
gorithm from the representation theory of the symmetric group. A lot of wor
k has been devoted to the length k of the longest increasing subsequence of
a permutation 1\,2\, ... \, n\, beginning with Ulam's question of determin
ing the average value of this number over all such permutations. There are
many interesting analogues of longest increasing subsequences\, such as lon
gest alternating subsequences\, i.e.\, subsequences b_1\,b_2\, ... \, b_k o
f a permutation a_1\, a_2\, ... \, an satisfying b_1>b_2b_4< ... . We
will survey these highlights of the remarkable theory of increasing and dec
reasing subsequences.\n\n__________________________________________\n\nRich
ard Stanley is Professor Emeritus of Mathematics\, MIT\, since January 2018
. He received the B.S. in mathematics from Caltech in 1966\, and the Ph.D.
in mathematics from Harvard University in 1971\, under the direction of Gia
n-Carlo Rota. He joined the MIT faculty in applied mathematics in 1973\, an
d became a professor in 1979. Professor Stanley's research concerns problem
s in algebraic combinatorics. Professor Stanley's distinctions include the
SIAM George Pólya Prize in applied combinatorics\, 1975\, a Guggenheim fell
owship\, 1983\, the Leroy P. Steele Prize for Mathematical Exposition\, 200
1\, the Rolf Schock Prize in Mathematics\, 2003\, and the Aisenstadt Chair\
, University of Montreal\, 2007. Stanley was the inaugural holder of the De
partment's Levinson Professorship Chair of Mathematics\, 2000-2010. He was
appointed Senior Scholar at the Clay Mathematics Institute in 2004\, and re
ceived the Honorary Doctor from the University of Waterloo. In 2007\, he re
ceived an Honorary Professorship from Nankai University. He is a Fellow of
the American Academy of Arts & Sciences (1988) and Member of the National A
cademy of Sciences (1995).
DTEND:20181127T010000Z
DTSTAMP:20201127T150658Z
DTSTART:20181127T000000Z
GEO:34.022631;-118.290533
LOCATION:Irani Hall (RRI)\, 101
SEQUENCE:0
SUMMARY:Whiteman Memorial Mathematics Lectures Joint with CAMS Distinguishe
d Lecture: Increasing and decreasing subsequences
UID:tag:localist.com\,2008:EventInstance_4109026
URL:https://calendar.usc.edu/event/whiteman_memorial_mathematics_lectures_j
oint_with_cams_distinguished_lecture_increasing_and_decreasing_subsequences
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