2005 Kemeny Lecture Series 
Andrew Granville
Universite de Montreal
will give the following series of lectures
An introduction to additive
combinatorics
Thursday, April 21, 2005
4:00 - 5:00 pm
102 Bradley Hall
(Tea 3:30 pm Math Lounge)
Abstract: The birth of a new subject can rarely have been so
spectacular as the
developments in the last few years in "additive combinatorics", a
blend of combinatorics, harmonic analysis, discrete geometry, graph
theory, group theory, analytic number theory, ergodic theory,
probability theory, ... . What with Gowers' new and explicit
proof
of Szemeredi's theorem developing a new type of harmonic analysis,
Bourgain's amazing exponential sum estimates, and the proof of Green
and Tao that there are infinitely many k-term arithmetic
progressions of primes, it is clear that there is enormous potential
in this new area. In this talk we will introduce the central concerns,
and maybe one or two proofs "from the book", attempting to use ideas
from all of the subject areas named above!
Note: This talk will be accessible to graduate students.
NB: A PDF
version of this abstract (suitable for posting) is also available.
Prime Number Races
Thursday, April 21, 2005
6:30 - 7:30 pm
L02 Carson Hall
Abstract: There's nothing quite like a day at the races
... . The quickening of the pulse as the starter's pistol sounds,
the thrill when your favorite contestant speeds out into the lead (or
the distress if another contestant dashes out ahead of yours), and the
accompanying fear (or hope) that the leader might change. And what if
the race is a marathon? Maybe one of the contestants will be far
stronger than the others, taking the lead and running at the head of
the pack for the whole race. Or perhaps the race will be more
dramatic, with the lead changing again and again.
Our race
involves the odd prime numbers, divided into two teams. Come to
this
talk to learn more about these races, and hear the speaker's analysis
of which team he expects to win and why.
Note: This talk is for a general audience and will be
accessible to undergraduates.
NB: A PDF
version of this announcement (suitable for posting) is also
available.
Pretentious characters and
the Polya-Vinogradov theorem
Friday, April 22, 2005
4:00 - 5:00 pm
102 Bradley Hall
(Tea 3:30 pm Math Lounge)
Abstract: The Polya-Vinogradov theorem is one of the
central estimates of analytic number theory. There had not been any
significant improvement in this theorem since 1919 until the speaker
and Soundararajan did so in the last few weeks. Part of the story is
to gain a much sharper understanding of large character sums (which
only occur if pretentious characters get involved), and part of it
involves the definition of a "new" norm on high-dimensional tori.
This talk will outline the proof and focus on the potential
applications of this norm.
Note: This talk will be accessible to graduate students.
NB: A PDF
version of this announcement (suitable for posting) is also
available.