Physics Colloquium: Twin primes in function fields

Abstarct:

Number theory is concerned with the arithmetic properties of the integers. Prime numbers are the building blocks of the  integers, and since ancient times they have attracted the attention of mankind. Although the proof of the infinitude of  prime numbers already appears in Elements of Euclid, it is still an open question today whether there is an infinity of twin primes [e.g. (3,5) or (59,61)].

Early in the development of number theory, it was observed that there is a deep analogy between the integers and the polynomials over a finite field with q elements, which has many applications in coding theory, cryptography, and other subjects.

In this talk I will describe this analogy between the two worlds, and present some of the recent results in number theory in the limit when q tends to infinity.

Seminar Organisers: Dr. Tomer Volansky, Dr. Dovi Poznanski