--------------------------------------------------------------
THE IVAN and BETTY NIVEN
DISTINGUISHED LECTURES
Next week the Department of Mathematics is hosting the first
Ivan and Betty Niven Distinguished Lectures, generously funded
by a bequest from Ivan and Betty Niven. This year the
three lectures will be given by Carl Pomerance, a well-known
analytic and computational number theorist. Carl has a
knack
of explaining subtle ideas at a level appropriate to his
audience so the lectures, especially the first two, should
be accessible to a wide audience, including students.
For full details, see
http://www.math.ubc.ca/~boyd/niven.html
He will be giving the lectures on March 21st, 22nd and 23rd.
The titles and abstracts are below.
The colloquium on Monday will be followed by a reception in
Matx 1115 from 4:00-6:00 PM. All are welcome.
Refreshments
will be provided.
Note that the lecture on Tuesday is aimed at students so please
advertise this to your classes, especially 3rd and 4th year and
graduate courses.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Monday, March 21, 3:00-4:00, MATX 1100
Joint IAM-Mathematics Colloquium
Title: A New Primal Screen
Abstract: How fast can one determine if a given number
is prime or composite? This question, which was first
posed explicitly by Gauss in 1801, has been the subject
of much attention in the computer age. In 2002, Agrawal,
Kayal and Saxena announced a new and surprisingly
simple deterministic algorithm that runs in polynomial
time (within a fixed power of the number of digits of
the number in question). We will discuss this algorithm
as well as more recent developments.
RECEPTION AND REFRESHMENTS, Monday, March 21, 4:00-6:00, MATX
1115
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Tuesday, March 22, 12:30-2:00, MATH 100
Student Lecture
(intended for graduate and advanced undergraduate students)
Title: Unsolved prime-number problems
Abstract: From the twin-prime conjecture to Goldbach's
conjecture and the Riemann Hypothesis, there are plenty
of unsolved problems related to prime numbers. In this
talk we will discuss these and more, including recent
progress.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Wednesday, March 23, 3:00-4:00, WMAX 110
Number Theory Seminar
Title: Periods of pseudorandom number
generators
Abstract: This talk will consider two common pseudorandom
number generators based in number theory. The first, due to
D.H. Lehmer, is the linear congruential generator, where the
$n+1$-st iterate $x_{n+1}$ is $ax_n+b\bmod m$ (where
$a,b,m$ and an initial seed $x_0$ are given. This generator
is commonly used in numerical analysis for Monte Carlo
simulations. The other is the power generator $x_{n+1}=x_n^a\bmod
m$,
where $a,m$ and $x_0$ are given. This generator has
cryptographic applications. Among other results we have
that for any nontrivial choice of parameters $a,b,x_0$, the linear
congruential generator has period $m/\exp((1+o(1))\log\log m\log\log\log
m)$
for almost all $m$, while the power generator has period
$m/\exp((1+o(1))(\log\log m)^2\log\log\log m)$ for almost all $m$.
These results, which are conditional on the Generalized Riemann
Hypothesis,
are joint with Par Kurlberg, Shuguang Li, and Greg Martin.
![[IMAGE: MAA Logo]](maalogo.gif)
Link to the MAA Home Page
Maintained by Afton
H. Cayford, at The University of British Columbia.
Return to the Home Page
Last updated 15 March, 2005