Dartmouth 2000 Kemeny Lecture Series MATH

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.