# 2000 Kemeny Lecture Series

## Andrew Odlyzko

### AT&T

will give the following series of lectures

## Primes: What we do and don't know

### Monday, May 1, 2000

### 7:00 - 8:00 pm

### Moore Psychology Auditorium B3

**Abstract.**
The distribution of primes has fascinated mathematicians, amateurs and
professionals alike, for thousands of years. While tremendous
progress has been achieved, we still cannot answer such basic
questions as to whether there exist infinitely many twin primes, that
is primes p for which p+2 is also a prime. Furthermore, prime number
theory abounds in conjectures that were supported by extensive
experiments and heuristics, but in the end were shown to be false.
**Note:** This talk is intended for everyone, including undergraduates.

## Zeros of the Riemann zeta function: Conjectures
and computations

### Tuesday, May 2

### 4:00 - 5:00 pm

### Rockefeller Center Room 3

### (Tea 3:30 pm Math Lounge)

**Abstract:** The Riemann Hypothesis is now the most famous
unsolved problem in mathematics. It has stimulated extensive
computations, including development of novel algorithms that are
similar to those used in astrophysical simulations and in signal
processing. These computations have so far confirmed the predictions
of the Riemann Hypothesis, as well as of other, even more speculative
conjectures. However, there is still a serious question of what these
results mean.

## Polynomials with restricted coefficients: results
& open problems

### Wednesday, May 3

### 4:00 - 5:00 pm

### Rockefeller Center Room 3

### (Tea 3:30 pm Math Lounge)

**Abstract: ** Many applications in acoustics, communication
theory, and analysis require finite sequences of 0s and 1s or +-1s
that have special autocorrelation properties. These properties are
often equivalent to conditions on the polynomials with that sequence
as coefficients. While there are many constructions and theorems
known, some of the most intriguing problems remain wide open, and
extensive computer searches with special algorithms are often used to
search for the best sequences.
**Host: **Prof. Dan Rockmore will be hosting the speaker while he
is visiting Dartmouth. Please contact Dan at #646-3260 if you would
like to meet the speaker during his visit.