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Re: Countdown to the 2010 Fields medal(s)
Posted:
Aug 16, 2010 2:04 AM
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Part 12 of my comments on the
26-th International Congress of Mathematicians
(ICM2010), that will be held in Hyderabad, in India,
from Thursday, August 19, to Friday, August 27, 2010.
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Before I continue giving more information about
the ICM2010, I recall that:
The original posting of this thread of postings
is posted on the following Web page:
http://mathforum.org/kb/message.jspa?messageID=7137304&tstart=60
The Web site of the ICM2010 is the following:
http://www.icm2010.org.in/
I guess that the names of the winners of the Fields
medals and other prizes will be posted on Thursday,
August 19 on the following Web page of press releases
of the ICM2010:
http://www.icm2010.org.in/press-room/press-releases
In my previous posting, on the following Web page:
http://mathforum.org/kb/message.jspa?messageID=7152442&tstart=60
I have started to gather some pieces of information
about Ngô Bao Châu who has chances to be awarded
a Fields medal on August 19, that is, in three days.
In this posting, I continue to gather
more information about him.
=================================
1. There is a thread on sci.math started by
Marko Amnell
Ngo's proof of the fundamental lemma
Posted: Dec 14, 2009 12:50 AM
about Ngô Bao Châu. It is posted on the following
Web page:
http://mathforum.org/kb/message.jspa?messageID=6927897&tstart=0
=================================
2. Here are pieces of information extracted from
the following Web page of the Web site
of the Clay Mathematics Institute:
http://claymath.org/research_award/Laumon-Ngo/
Clay Research Award 2004 was awarded to Gérard Laumon
and Bao-Châu Ngô for their proof of the Fundamental
Lemma for unitary groups. Gérard Laumon was the Ph.D.
thesis advisor of Bao-Châu Ngô.
The lemma is a conjectured identity between orbital
integrals for two groups, e.g., the unitary groups
U(n) and U(p)xU(q), where p+q = n.
Combined with the Arthur-Selberg trace formula,
it enables one to prove relations between automorphic
forms on different groups and is a key step towards
proving links between certain automorphic forms
and Galois representations.
This is one of the aims of the Langlands program,
which seeks a far-reaching unification of ideas
in number theory and representation theory.
The result of Laumon and Ngô uses the equivariant
cohomology approach introduced by Goresky, Kottwitz,
and MacPherson, who proved the lemma in the split
and equal valuation case.
The proof for the unitary case, requires many
new ideas, including Laumon's deformation strategy
and Ngô's purity result, which is based on a geometric
interpretation of the endoscopy theory of Langlands
and Kottwitz in terms of the Hitchin fibration.
=================================
3. Here are additional pieces of information
extracted from the following Web page, on the
Web site of the Clay Mathematics Institute:
http://claymath.org/research_award/
The Langlands program is a collection of conjectures
and theorems that unify the theory of automorphic
forms, relating it intimately to the main stream
of number theory, with close relations to harmonic
analysis on algebraic groups as well as arithmetic
algebraic geometry.
Since its origins in the winter of 1966-67,
when it was laid out in a letter from Langlands
to André Weil, it has served as the basis of much
deep work, including applications to many famous
problems in number theory,
e.g., Artin's conjectures on L-functions,
Fermat's Last Theorem,
and the behaviour of Hasse-Weil zeta functions.
=================================
4. Here are pieces of information extracted
from the following Web page on the Web site
of the University of Chicago:
http://news.uchicago.edu/news.php?asset_id=1848
Ngô Bao Châu has accepted a faculty appointment
at the University of Chicago. He will become
a professor of mathematics there,
effective Sept. 1, 2010.
Ngô Bao Châu made one of Time magazine's top 10
scientific discoveries of 2009.
Langlands tried to prove the fundamental lemma
during the 1970s. In later years, the University
of Chicago's Robert Kottwitz and three colleagues
from other institutions developed approaches
to the problem. Peter Constantin said Ngô Bao Châu
"added numerous striking ideas" to their work
in "a 200-page masterpiece."
The opportunity to work more closely
with colleagues at the University of Chicago
"certainly has a lot to do with my decision
to come to Chicago," Ngô Bao Châu said.
"People are addressing some of the most
fundamental questions in mathematics
at the Department of Mathematics
of the University of Chicago.
I have been having a mathematical conversation
with Bob Kottwitz for many years. I count
on the pleasure of pursing this conversation
with him for the years to come."
In addition to Kottwitz, William J. Friedman
and Alicia Townsend Friedman, Ngô Bao Châu
said he had learned a lot from Vladimir Drinfeld,
as well as a host of other University Chicago
mathematicians whose specialties are closely
allied with his: Alexander Beilinson, David
and Mary Winton Green, Spencer Bloch,
Victor Ginzburg, Kazuya Kato, and Madhav Nori.
=================================
The Web page of Ngô Bao Châu
at the Université Paris-Sud in France
is the following:
http://www.math.u-psud.fr/~ngo/
=================================
Piece of information extracted from
the following Web page:
https://www.math.ias.edu/node/30
Ngô Bao Châu is currently a member of
the School of Mathematics
of the Institute for Advanced Study
at Princeton, New Jersey, USA
======================
Countdown: The Fields medals 2010
will be awarded in 3 days,
on Thursday, August 19, 2010.
======================
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